Results of Elliptic Integrals II
This is the second half of the chapter Elliptic Integrals. It shows results from Section 19.22 to 19.36. For Section 19.1 to 19.21 go to Elliptic Integrals I.
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 19.22.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+(x)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+x*y)*sqrt(t+(a)^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Aborted | Failure | Skipped - Because timed out | Failed [102 / 108]
{Complex[0.1731783664325578, 0.8740191847640398] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Complex[0.4406854652170371, 0.9732684211375591] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]} |
| 19.22.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*Sqrt[(y)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4*Sqrt[(a)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Complex[-0.848574889541176, -1.6278775384876862] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}-2.356194490192345 <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*(y)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))*((y)^(2)-0)^(1/2)) == Divide[1,4]*((y)^(2)- (x)^(2))* 3*(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/(((a)^(2)-x*y)*((a)^(2)-0)^(1/2))+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)} | Error |
(p(Subscript[p, +])^(2)- p(Subscript[p, -])^(2))* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 3*((a)^(2)-0)/((a)^(2)-p(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-p(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p) |
Missing Macro Error | Failure | - | Error |
| 19.22.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)} | Error |
(p(Subscript[p, -])^(2)- p(Subscript[p, +])^(2))* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 3*((a)^(2)-0)/((a)^(2)-p(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-p(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p) |
Missing Macro Error | Failure | - | Error |
| 19.22#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}p_{-} = pa} | p[+]*p[-] = p*a |
Subscript[p, +]*Subscript[p, -] == p*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}+p_{-}^{2} = p^{2}+xy} | (p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y |
(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}} | (p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))) |
(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}} | (p(p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2) |
(p(Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*(p)^(2)* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]*3*((a)^(2)-0)/((a)^(2)-v(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-v(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Error |
| 19.22.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0])) |
Error |
Aborted | Missing Macro Error | Skipped - Because timed out | - |
| 19.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)} | (a(a[0])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 0..infinity)) (a(a[1])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 2..infinity)) |
Error |
Failure | Missing Macro Error | Error | - |
| 19.22#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1} | Q[0] = 1 |
Subscript[Q, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}} | Q[n + 1] = (1)/(2)*Q[n]*(a[n]- g[n])/(a[n]+ g[n]) |
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}} | p[n + 1] (p(p[n])^(2)+ a[n]*g[n])/(2*p[n]) |
Subscript[p, n + 1] Divide[p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}} | (p(p[n])^(2)- a[n]*g[n])/(p(p[n])^(2)+ a[n]*g[n]) |
Divide[p(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1} | Q[0] = 1 |
Subscript[Q, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}} | Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n] |
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})} | (p[0])^(2) (q(q[0])^(2)+ a(a[0])^(2)) |
(Subscript[p, 0])^(2) (q(Subscript[q, 0])^(2)+ a(Subscript[a, 0])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = (x+y)/2} | a = (x + y)/ 2 |
a == (x + y)/ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}} | 2*x + y*I[+] = sqrt(((x + y*I)+ x)*((x + y*I)+ y))+sqrt(((x + y*I)- x)*((x + y*I)- y)) |
2*Subscript[x + y*I, +] == Sqrt[((x + y*I)+ x)*((x + y*I)+ y)]+Sqrt[((x + y*I)- x)*((x + y*I)- y)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}z_{-} = za} | z[+]*z[-] = z*a |
Subscript[z, +]*Subscript[z, -] == z*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}+z_{-}^{2} = z^{2}+xy} | (x + y*I[+])^(2)+(x + y*I[-])^(2) = (x + y*I)^(2)+ x*y |
(Subscript[x + y*I, +])^(2)+(Subscript[x + y*I, -])^(2) == (x + y*I)^(2)+ x*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}} | (x + y*I[+])^(2)-(x + y*I[-])^(2) = sqrt(((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))) |
(Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2) == Sqrt[((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}} | ((x + y*I)(x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2) |
((x + y*I)(Subscript[x + y*I, +])^(2)- (a)^(2)) == (Sqrt[(x + y*I)^(2)- (x)^(2)]+Sqrt[(x + y*I)^(2)- (y)^(2)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}} | 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I)(x + y*I[-])^(2))*sqrt(t+(x + y*I)(x + y*I[+])^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2)] |
Error | Failure | - | Error |
| 19.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)} | Error |
((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))* 3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) 3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))])/(((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))*((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I)) |
Missing Macro Error | Failure | - | Error |
| 19.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)} | Error |
((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))* 3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) 3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/(((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I)) |
Missing Macro Error | Failure | - | Error |
| 19.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}} | Error |
(p(Subscript[p, +])^(2)- p(Subscript[p, -])^(2))* 3*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, +])^(2))*(EllipticPi[((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))] |
Missing Macro Error | Failure | - | Error |
| 19.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}} | Error |
(p(Subscript[p, -])^(2)- p(Subscript[p, +])^(2))* 3*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, -])^(2))*(EllipticPi[((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, -])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))] |
Missing Macro Error | Failure | - | Error |
| 19.22.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z} | Error |
2*Sqrt[(x + y*I)^(2)-(x)^(2)]*(EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]^2]) Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]-(x + y*I) |
Missing Macro Error | Failure | - | Error |
| 19.22.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}} | Error |
1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+y = 2a} | x + y = 2*a |
x + y == 2*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}} | x - y sqrt(((a)^(2)-(x + y*I)(x + y*I[+])^(2))*((a)^(2)-(x + y*I)(x + y*I[-])^(2))) |
x - y Sqrt[((a)^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))*((a)^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \ifrac{z_{+}z_{-}}{a}} | z = (z[+]*z[-])/(a) |
z == Divide[Subscript[z, +]*Subscript[z, -],a] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.23.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{z} = \int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-1/2}\diff{\theta}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = int((y*(cos(theta))^(2)+(x + y*I)*(sin(theta))^(2))^(- 1/ 2), theta = 0..Pi/ 2) |
EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] == Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(- 1/ 2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Aborted | Failure | Skipped - Because timed out | Failed [18 / 18]
{Complex[0.8397393007192011, 1.792316631638506] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-1.057179647328743, -0.8381019542468571] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.23.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{0}{y}{z} = \frac{1}{2}\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{1/2}\diff{\theta}} | Error |
Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) == Divide[1,2]*Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(1/ 2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[0.5014070071339144, -0.6068932953779227], Times[Complex[1.345607733249115, -0.5573689727459014], Plus[Complex[1.465481142300126, -0.24396122198922798], Times[Complex[0.2643318009908678, -0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Plus[Complex[-0.9996439786591846, -0.22609983985234913], Times[Complex[1.345607733249115, 0.5573689727459014], Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{0}{y}{z} = 3\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-3/2}\sin^{2}@@{\theta}\diff{\theta}} | Error |
3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2)) == 3*Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(- 3/ 2)* (Sin[\[Theta]])^(2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta}} | Error |
EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] == Divide[2,Pi]*Integrate[1/Sqrt[(x + y*I)* (Cos[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + y*I)* (Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta} = \frac{2}{\pi}\int_{0}^{\infty}\CarlsonellintRC@{y\cosh^{2}@@{t}}{z}\diff{t}} | Error |
Divide[2,Pi]*Integrate[1/Sqrt[(x + y*I)* (Cos[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + y*I)* (Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] == Divide[2,Pi]*Integrate[1/Sqrt[x + y*I]*Hypergeometric2F1[1/2,1/2,3/2,1-(y*(Cosh[t])^(2))/(x + y*I)], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{x}{y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta}}\diff{\theta}} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == Divide[2,Pi]*Integrate[1/Sqrt[y*(Cos[\[Theta]])^(2)+(x + y*I)* (Sin[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y*(Cos[\[Theta]])^(2)+(x + y*I)* (Sin[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\pi\CarlsonsymellintRF@{x}{y}{z} = \int_{0}^{2\pi}\!\!\!\!\int_{0}^{\pi}\frac{\sin@@{\theta}\diff{\theta}\diff{\phi}}{(x\sin^{2}@@{\theta}\cos^{2}@@{\phi}+y\sin^{2}@@{\theta}\sin^{2}@@{\phi}+z\cos^{2}@@{\theta})^{1/2}}} | 4*Pi*0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = int(int((sin(theta))/((x*(sin(theta))^(2)* (cos(phi))^(2)+ y*(sin(theta))^(2)* (sin(phi))^(2)+(x + y*I)*(cos(theta))^(2))^(1/ 2)), theta = 0..Pi), phi = 0..2*Pi) |
4*Pi*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == Integrate[Integrate[Divide[Sin[\[Theta]],(x*(Sin[\[Theta]])^(2)* (Cos[\[Phi]])^(2)+ y*(Sin[\[Theta]])^(2)* (Sin[\[Phi]])^(2)+(x + y*I)*(Cos[\[Theta]])^(2))^(1/ 2)], {\[Theta], 0, Pi}, GenerateConditions->None], {\[Phi], 0, 2*Pi}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.23.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{x}{y}{z} = \frac{1}{4}\int_{0}^{\infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\*\left(\frac{x}{t+x}+\frac{y}{t+y}+\frac{z}{t+z}\right)t\diff{t}} | Error |
Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == Divide[1,4]*Integrate[Divide[1,Sqrt[t + x]*Sqrt[t + y]*Sqrt[t +(x + y*I)]]*(Divide[x,t + x]+Divide[y,t + y]+Divide[x + y*I,t +(x + y*I)])* t, {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}} | ln(4) <= sqrt(x + y*I)*0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)+ ln(sqrt(y/(x + y*I))) |
Log[4] <= Sqrt[x + y*I]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]+ Log[Sqrt[y/(x + y*I)]] |
Error | Failure | - | Failed [9 / 9]
{LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[1.3862943611198906, Complex[0.6277320470267476, -0.9602476282953896]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi} | sqrt(x + y*I)*0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)+ ln(sqrt(y/(x + y*I))) <= (1)/(2)*Pi |
Sqrt[x + y*I]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]+ Log[Sqrt[y/(x + y*I)]] <= Divide[1,2]*Pi |
Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[0.6277320470267476, -0.9602476282953896], 1.5707963267948966] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}} | Error |
Divide[1,2] <= (x + y*I)^(- 1/ 2)* Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[0.5, Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[0.5, Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi} | Error |
(x + y*I)^(- 1/ 2)* Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) <= Divide[1,4]*Pi |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}} | Error |
(Divide[(y)^(3/ 2)+(x + y*I)^(3/ 2),2])^(2/ 3) <= Divide[4,Pi]*Sqrt[(x + y*I)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(x + y*I)^(2)]]]^2]) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[1.0588191704631045, 0.29794136993360365], Complex[2.118851869395612, 0.5983245902184247]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}} | Error |
Divide[4,Pi]*Sqrt[(x + y*I)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(x + y*I)^(2)]]]^2]) <= (Divide[(y)^(2)+(x + y*I)^(2),2])^(1/ 2) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[2.118851869395612, 0.5983245902184247], Complex[1.112897508375995, 0.3369582528288897]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}} | Error |
Divide[2,Sqrt[p]]*(2*y*(x + y*I)+ y*p +(x + y*I)*p)^(- 1/ 2) <= Divide[4,3*Pi]*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7797231369520263, -0.6247258696161743], Complex[-0.6706782382611747, 0.54526856836685]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}} | Error |
Divide[4,3*Pi]*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] <= (y*(x + y*I)*(p)^(2))^(- 3/ 8) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.6706782382611747, 0.54526856836685], Complex[0.8422602311268256, -0.6912251080442312]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}} | (1)/(a[n]) 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) |
Divide[1,Subscript[a, n]] EllipticF[ArcCos[Sqrt[0/g(Subscript[g, 0])^(2)]],(g(Subscript[g, 0])^(2)-a(Subscript[a, 0])^(2))/(g(Subscript[g, 0])^(2)-0)]/Sqrt[g(Subscript[g, 0])^(2)-0] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300] {LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]]] <- {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[-0.4999999999999998, -0.8660254037844387], g], Rational[-1, 2]], EllipticK[Times[Complex[-1.9999999999999991, 3.464101615137755], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[-0.124
|
| 19.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) <= (1)/(g[n]) |
EllipticF[ArcCos[Sqrt[0/g(Subscript[g, 0])^(2)]],(g(Subscript[g, 0])^(2)-a(Subscript[a, 0])^(2))/(g(Subscript[g, 0])^(2)-0)]/Sqrt[g(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300] {LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]], Complex[1.7320508075688774, -0.9999999999999999]] <- {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g,
|
| 19.24#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n+1} = (a_{n}+g_{n})/2} | a[n + 1] = (a[n]+ g[n])/ 2 |
Subscript[a, n + 1] == (Subscript[a, n]+ Subscript[g, n])/ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.24#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{n+1} = \sqrt{a_{n}g_{n}}} | g[n + 1] = sqrt(a[n]*g[n]) |
Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.24.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}} | Error |
L*(a , b) == 8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) |
Missing Macro Error | Failure | - | Error |
| 19.24#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}} | Error |
EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]*Sqrt[0-x]*(EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2*EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/0]]]^2]) > Divide[1,8]*(Pi)^(2) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Indeterminate, 1.2337005501361697] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Indeterminate, 1.2337005501361697] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi} | Error |
EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]+ 2*Sqrt[0-x]*(EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2*EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/0]]]^2]) > Pi |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Indeterminate, 3.141592653589793] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Indeterminate, 3.141592653589793] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}} | Error |
Divide[Sqrt[0-a(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]/Sqrt[0-a(Subscript[a, 0])^(2)]] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[-0.06249999999999997, -0.10825317547305484], Indeterminate] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}} | Error |
Divide[Sqrt[0-a(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]/Sqrt[0-a(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}} | (3)/(sqrt(x)+sqrt(y)+sqrt(x + y*I)) <= 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
Divide[3,Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]] <= EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Error | Failed [18 / 18]
{LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7738030002696183, -0.11364498174072818], Complex[-0.28823404661462, -0.7809212115368181]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) <= (1)/((x*y*(x + y*I))^(1/ 6)) |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] <= Divide[1,(x*y*(x + y*I))^(1/ 6)] |
Aborted | Failure | Error | Failed [18 / 18]
{LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.7640769591692358, -0.10059264002361257]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}} | Error |
(Divide[5,Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]+ 2*Sqrt[p]])^(3) <= 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7477899794343462, -0.4392695700678081], Complex[-0.36602768453446033, 0.5058947820270108]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}} | Error |
3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] <= (x*y*(x + y*I)*(p)^(2))^(- 3/ 10) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.36602768453446033, 0.5058947820270108], Complex[0.8086249764673956, -0.49552602288885395]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}} | Error |
Divide[1,3]*(Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]) <= Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[0.8567842015469013, 0.22245863288189585], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[1.2650324920107643, 0.1857896575819671], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 1 |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Times[Complex[0.44712810031579164, 0.7279709757493625], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Times[Complex[0.42667960094115687, -0.925915614148855], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]+ Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 2 |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Plus[Complex[-0.16214470973156064, 0.6784437678906974], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Plus[Complex[-0.28823404661462, -0.7809212115368181], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}} | Error |
1/Sqrt[Divide[1,2]*(y +(x + y*I))]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Divide[1,2]*(y +(x + y*I)))] <= EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7805167095081702, -0.12346643314922054], Complex[-0.28823404661462, -0.7809212115368181]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] <= 1/Sqrt[Sqrt[y*(x + y*I)]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Sqrt[y*(x + y*I)])] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.765857524311696, -0.1031964554328576]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.25#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \CarlsonsymellintRF@{0}{{k^{\prime}}^{2}}{1}} | EllipticK(k) = 0.5*int(1/(sqrt(t+0)*sqrt(t+1 - (k)^(2))*sqrt(t+1)), t = 0..infinity) |
EllipticK[(k)^2] == EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]/Sqrt[1-0] |
Failure | Failure | Error | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[-0.16657773258291342, -1.0782578237498217] <- {Rule[k, 2]} |
| 19.25#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = 2\CarlsonsymellintRG@{0}{{k^{\prime}}^{2}}{1}} | Error |
EllipticE[(k)^2] == 2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{-2.820197789027711 <- {Rule[k, 1]}Complex[-4.864068276731299, 1.343854231387098] <- {Rule[k, 2]} |
| 19.25#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \tfrac{1}{3}{k^{\prime}}^{2}\left(\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}+\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}\right)} | Error |
EllipticE[(k)^2] == Divide[1,3]*1 - (k)^(2)*(3*(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))*(1-0)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)*(1 - (k)^(2)-0)^(1/2))) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[7.885081986624734, -2.293856789051463] <- {Rule[k, 2]} |
| 19.25#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k}-\compellintEk@{k} = k^{2}\compellintDk@{k}} | EllipticK(k)- EllipticE(k) = (k)^(2)* (EllipticK(k) - EllipticE(k))/(k)^2 |
EllipticK[(k)^2]- EllipticE[(k)^2] == (k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] |
Successful | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[0.3274322182097533, -1.81658404135269] <- {Rule[k, 2]} |
| 19.25#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}\compellintDk@{k} = \tfrac{1}{3}k^{2}\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}} | Error |
(k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] == Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))*(1-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[-1.5165865988698335, -0.6055280137842299] <- {Rule[k, 2]} |
| 19.25#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k} = \tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}} | Error |
EllipticE[(k)^2]-1 - (k)^(2)*EllipticK[(k)^2] == Divide[1,3]*(k)^(2)*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)*(1 - (k)^(2)-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-2.3636107378197124, 2.0191745059478237] <- {Rule[k, 2]} |
| 19.25.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k}-\compellintKk@{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{0}{{k^{\prime}}^{2}}{1}{1-\alpha^{2}}} | Error |
EllipticPi[\[Alpha]^(2), (k)^2]- EllipticK[(k)^2] == Divide[1,3]*\[Alpha]^(2)* 3*(1-0)/(1-1 - \[Alpha]^(2))*(EllipticPi[(1-1 - \[Alpha]^(2))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0] |
Missing Macro Error | Failure | - | Failed [9 / 9]
{Indeterminate <- {Rule[k, 1], Rule[α, 1.5]}Complex[-1.5241433161083033, 0.5547659663605348] <- {Rule[k, 2], Rule[α, 1.5]} |
| 19.25.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = -\tfrac{1}{3}(k^{2}/\alpha^{2})\CarlsonsymellintRJ@{0}{1-k^{2}}{1}{1-(k^{2}/\alpha^{2})}} | Error |
EllipticPi[\[Alpha]^(2), (k)^2] == -Divide[1,3]*((k)^(2)/ \[Alpha]^(2))* 3*(1-0)/(1-1 -((k)^(2)/ \[Alpha]^(2)))*(EllipticPi[(1-1 -((k)^(2)/ \[Alpha]^(2)))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0] |
Missing Macro Error | Failure | - | Skip - No test values generated |
| 19.25.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | EllipticF(sin(phi), k) = 0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1] |
Failure | Failure | Failed [180 / 180] 180/180]: [[Float(undefined)+Float(undefined)*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 1}3.854689052+3.461698034*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [180 / 180]
{Complex[2.0026000841930385, 1.2187088711714384] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.4748265293714395, 0.7583435972865697] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintFk@{\phi}{k}}{k} = \tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}} | Error |
D[EllipticF[\[Phi], (k)^2], k] == Divide[1,3]*k*3*(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)*(c - (k)^(2)-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Indeterminate <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.4045300788217367, 0.4404710702025501] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = 2\CarlsonsymellintRG@{c-1}{c-k^{2}}{c}-(c-1)\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\sqrt{(c-1)(c-k^{2})/c}} | Error |
EllipticE[\[Phi], (k)^2] == 2*Sqrt[c-c - 1]*(EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+(Cot[ArcCos[Sqrt[c - 1/c]]])^2*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+Cot[ArcCos[Sqrt[c - 1/c]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[c - 1/c]]]^2])-(c - 1)* EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Sqrt[(c - 1)*(c - (k)^(2))/ c] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[5.787775994567906, 4.022803158659452] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[6.805668366738806, 3.968311704298834] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[3.5743811704478246, 0.7698502565730785] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[3.9424508382496875, -1.017653751864599] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = {k^{\prime}}^{2}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}+k^{2}\sqrt{(c-1)/(c(c-k^{2}))}} | Error |
EllipticE[\[Phi], (k)^2] == 1 - (k)^(2)*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]+Divide[1,3]*(k)^(2)*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)*(c - (k)^(2)-c - 1)^(1/2))+ (k)^(2)*Sqrt[(c - 1)/(c*(c - (k)^(2)))] |
Missing Macro Error | Failure | - | Failed [20 / 20]
{Complex[-1.0687219916023158, 0.8637282710955538] <- {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.7724732696890155, 1.0672164584507502] <- {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = -\tfrac{1}{3}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-k^{2}}{c}{c-1}+\sqrt{(c-k^{2})/(c(c-1))}} | Error |
EllipticE[\[Phi], (k)^2] == -Divide[1,3]*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))]-EllipticE[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))])/((c - 1-c)*(c - 1-c - (k)^(2))^(1/2))+Sqrt[(c - (k)^(2))/(c*(c - 1))] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[3.6312701919621486, -1.3602272606820804] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.7754142926962797, -0.6029933704091625] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintEk@{\phi}{k}}{k} = -\tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
D[EllipticE[\[Phi], (k)^2], k] == -Divide[1,3]*k*3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[1.571781086254786, -0.44885861459835996] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.233812154439124, -0.8879986745755843] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{\phi}{k} = \tfrac{1}{3}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4] == Divide[1,3]*3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[-1.571781086254786, 0.44885861459835996] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6083725296430629, 0.41279951787826946] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\alpha^{2}}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2] == Divide[1,3]*\[Alpha]^(2)* 3*(c-c - 1)/(c-c - \[Alpha]^(2))*(EllipticPi[(c-c - \[Alpha]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-0.9803588804354156, -0.9579910370435353] <- {Rule[c, -1.5], Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6164275583611891, -0.384238714210872] <- {Rule[c, -1.5], Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k} = -\tfrac{1}{3}\omega^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\omega^{2}}+\sqrt{\frac{(c-1)(c-k^{2})}{(\alpha^{2}-1)(1-\omega^{2})}}\*\CarlsonellintRC@{c(\alpha^{2}-1)(1-\omega^{2})}{(\alpha^{2}-c)(c-\omega^{2})}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == -Divide[1,3]*\[Omega]^(2)* 3*(c-c - 1)/(c-c - \[Omega]^(2))*(EllipticPi[(c-c - \[Omega]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1]+Sqrt[Divide[(c - 1)*(c - (k)^(2)),(\[Alpha]^(2)- 1)*(1 - \[Omega]^(2))]]* 1/Sqrt[(\[Alpha]^(2)- c)*(c - \[Omega]^(2))]*Hypergeometric2F1[1/2,1/2,3/2,1-(c*(\[Alpha]^(2)- 1)*(1 - \[Omega]^(2)))/((\[Alpha]^(2)- c)*(c - \[Omega]^(2)))] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.11631142199526823, 0.9703799109463437] <- {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, -2]}Complex[-0.11631142199526823, 0.9703799109463437] <- {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, 2]} |
| 19.25.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{x}{y}{z}} | EllipticF(sin(phi), k) = 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Failed [300 / 300] 300/300]: [[2.547570015-.6488873983*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}2.209888328-.6080126261*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.5939484671297026, -0.40701440305540804] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.5587134153531784, -0.34669285510288844] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x,y,z) = (c-1,c-k^{2},c)} | (x , y ,(x + y*I)) = (c - 1 , c - (k)^(2), c) |
(x , y ,(x + y*I)) == (c - 1 , c - (k)^(2), c) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi = \acos@@{\sqrt{\ifrac{x}{z}}}} | phi = arccos(sqrt((x)/(x + y*I))) |
\[Phi] == ArcCos[Sqrt[Divide[x,x + y*I]]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[.806272406e-1+.9406867936*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}.806272406e-1+.593132064e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} |
Failed [180 / 180]
{Complex[-0.35238546150522904, 0.6906867935097715] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.0353981633974483, 0.8736994954019909] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{\sqrt{\ifrac{x}{z}}} = \asin@@{\sqrt{\ifrac{(z-x)}{z}}}} | arccos(sqrt((x)/(x + y*I))) = arcsin(sqrt(((x + y*I)- x)/(x + y*I))) |
ArcCos[Sqrt[Divide[x,x + y*I]]] == ArcSin[Sqrt[Divide[(x + y*I)- x,x + y*I]]] |
Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 19.25#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \sqrt{\frac{z-y}{z-x}}} | k = sqrt(((x + y*I)- y)/((x + y*I)- x)) |
k == Sqrt[Divide[(x + y*I)- y,(x + y*I)- x]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha^{2} = \frac{z-p}{z-x}} | (alpha)^(2) = ((x + y*I)- p)/((x + y*I)- x) |
\[Alpha]^(2) == Divide[(x + y*I)- p,(x + y*I)- x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{1/2}\CarlsonsymellintRF@{x}{y}{z} = \incellintFk@{\phi}{k}} | ((x + y*I)- x)^(1/ 2)* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = EllipticF(sin(phi), k) |
((x + y*I)- x)^(1/ 2)* EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == EllipticF[\[Phi], (k)^2] |
Aborted | Failure | Failed [300 / 300] 300/300]: [[-1.167656510+1.966567574*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}-.8299748231+1.925692802*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.015324342917649614, 0.4565416109140732] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.050559394694173865, 0.3962200629615536] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{3/2}\CarlsonsymellintRD@{x}{y}{z} = (3/k^{2})(\incellintFk@{\phi}{k}-\incellintEk@{\phi}{k})} | Error |
((x + y*I)- x)^(3/ 2)* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == (3/ (k)^(2))*(EllipticF[\[Phi], (k)^2]- EllipticE[\[Phi], (k)^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-0.9041684186949032, 0.18989946051507803] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.8729885067685752, 0.19149534336253457] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{3/2}\CarlsonsymellintRJ@{x}{y}{z}{p} = (3/\alpha^{2}){(\incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k})}} | Error |
((x + y*I)- x)^(3/ 2)* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == (3/ \[Alpha]^(2))*(EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-8.905365206673954*^-4, 0.6653826564189609] <- {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.030816807002235325, 0.6810951786851601] <- {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2(z-x)^{-1/2}\CarlsonsymellintRG@{x}{y}{z} = \incellintEk@{\phi}{k}+(\cot@@{\phi})^{2}\incellintFk@{\phi}{k}+(\cot@@{\phi})\sqrt{1-k^{2}\sin^{2}@@{\phi}}} | Error |
2*((x + y*I)- x)^(- 1/ 2)* Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == EllipticE[\[Phi], (k)^2]+(Cot[\[Phi]])^(2)* EllipticF[\[Phi], (k)^2]+(Cot[\[Phi]])*Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-1.8997799949200251, -0.4031557744461449] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-3.0701379688219372, -2.1411109504853227] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{n,d}) = k^{2}} | Delta*(n , d) = (k)^(2) |
\[CapitalDelta]*(n , d) == (k)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{d,c}) = {k^{\prime}}^{2}} | Delta*(d , c) = 1 - (k)^(2) |
\[CapitalDelta]*(d , c) == 1 - (k)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{n,c}) = 1} | Delta*(n , c) = 1 |
\[CapitalDelta]*(n , c) == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{u}{k} = \CarlsonellintRC@{\Jacobiellcsk^{2}@{u}{k}}{\Jacobiellnsk^{2}@{u}{k}}} | Error |
JacobiAmplitude[u, Power[k, 2]] == 1/Sqrt[(JacobiNS[u, (k)^2])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((JacobiCS[u, (k)^2])^(2))/((JacobiNS[u, (k)^2])^(2))] |
Missing Macro Error | Aborted | - | Failed [18 / 30]
{Complex[-0.5428587296705786, 0.8636075147962846] <- {Rule[k, 1], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}Complex[-0.6732377468613371, 0.8494366739388763] <- {Rule[k, 2], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u = \CarlsonsymellintRF@{\genJacobiellk{p}{s}^{2}@{u}{k}}{\genJacobiellk{q}{s}^{2}@{u}{k}}{\genJacobiellk{r}{s}^{2}@{u}{k}}} | u = 0.5*int(1/(sqrt(t+genJacobiellk(p)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(q)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(r)*(s)^(2)* u*k)), t = 0..infinity) |
u == EllipticF[ArcCos[Sqrt[genJacobiellk(p)*(s)^(2)* u*k/genJacobiellk(r)*(s)^(2)* u*k]],(genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(q)*(s)^(2)* u*k)/(genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(p)*(s)^(2)* u*k)]/Sqrt[genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(p)*(s)^(2)* u*k] |
Aborted | Failure | Error | Failed [300 / 300] {Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.78471422644353, -0.9906313764027224], Power[Times[Complex[-1.7426678688862403, -1.3308892896287465], genJacobiellk], Rational[-1, 2]]]] <- {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.3766936106342851, -1.225388931598258], Power[Times[Complex[-3.4853357377724805, -2.661778579257493], genJacobiellk], Rational[-1, 2]]]] <- {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Ration
|
| 19.26.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRF@{x}{y}{z}} | 0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity)+ 0.5*int(1/(sqrt(t+x + mu)*sqrt(t+y + mu)*sqrt(t+(x + y*I)+ mu)), t = 0..infinity) = 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]] == EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[0.6992255245511445, -1.8246422705609677] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.2162365888422955, -0.7585970772170993] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+\mu = \lambda^{-2}\left(\sqrt{(x+\lambda)yz}+\sqrt{x(y+\lambda)(z+\lambda)}\right)^{2}} | x + mu = (lambda)^(- 2)*(sqrt((x + lambda)* y*(x + y*I))+sqrt(x*(y + lambda)*((x + y*I)+ lambda)))^(2) |
x + \[Mu] == \[Lambda]^(- 2)*(Sqrt[(x + \[Lambda])* y*(x + y*I)]+Sqrt[x*(y + \[Lambda])*((x + y*I)+ \[Lambda])])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\xi,\eta,\zeta) = (x+\lambda,y+\lambda,z+\lambda)} | (xi , eta , zeta) = (x + lambda , y + lambda ,(x + y*I)+ lambda) |
(\[Xi], \[Eta], \[Zeta]) == (x + \[Lambda], y + \[Lambda],(x + y*I)+ \[Lambda]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \lambda^{-2}\left(\sqrt{xyz}+\sqrt{(x+\lambda)(y+\lambda)(z+\lambda)}\right)^{2}-\lambda-x-y-z} | mu = (lambda)^(- 2)*(sqrt(x*y*(x + y*I))+sqrt((x + lambda)*(y + lambda)*((x + y*I)+ lambda)))^(2)- lambda - x - y -(x + y*I) |
\[Mu] == \[Lambda]^(- 2)*(Sqrt[x*y*(x + y*I)]+Sqrt[(x + \[Lambda])*(y + \[Lambda])*((x + y*I)+ \[Lambda])])^(2)- \[Lambda]- x - y -(x + y*I) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\lambda\mu-xy-xz-yz)^{2} = 4xyz(\lambda+\mu+x+y+z)} | (lambda*mu - x*y - x*(x + y*I)- y*(x + y*I))^(2) = 4*x*y*(x + y*I)*(lambda + mu + x + y +(x + y*I)) |
(\[Lambda]*\[Mu]- x*y - x*(x + y*I)- y*(x + y*I))^(2) == 4*x*y*(x + y*I)*(\[Lambda]+ \[Mu]+ x + y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRD@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRD@{x}{y}{z}-\frac{3}{\sqrt{z(z+\lambda)(z+\mu)}}} | Error |
3*(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/(((x + y*I)+ \[Lambda]-y + \[Lambda])*((x + y*I)+ \[Lambda]-x + \[Lambda])^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]-EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])])/(((x + y*I)+ \[Mu]-y + \[Mu])*((x + y*I)+ \[Mu]-x + \[Mu])^(1/2)) == 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2))-Divide[3,Sqrt[(x + y*I)*((x + y*I)+ \[Lambda])*((x + y*I)+ \[Mu])]] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.4984590390126629, 1.2092907867192135] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.01924185171185039, 1.9974068077017313] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}+2\CarlsonsymellintRG@{x+\mu}{y+\mu}{z+\mu} = 2\CarlsonsymellintRG@{x}{y}{z}+\lambda\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\mu\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu}+\sqrt{\lambda+\mu+x+y+z}} | Error |
2*Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]*(EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]^2])+ 2*Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]]*(EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]+(Cot[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]+Cot[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]]^2]) == 2*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2])+ \[Lambda]*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ \[Mu]*EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]]+Sqrt[\[Lambda]+ \[Mu]+ x + y +(x + y*I)] |
Missing Macro Error | Aborted | - | Failed [300 / 300] {Plus[Complex[-2.0898920996046204, 0.6803615706262403], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[4.184639587172815, -1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-1.182728387586514, 0.2705509888970101], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038]
|
| 19.26.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+\CarlsonsymellintRJ@{x+\mu}{y+\mu}{z+\mu}{p+\mu} = \CarlsonsymellintRJ@{x}{y}{z}{p}-3\CarlsonellintRC@{\gamma-\delta}{\gamma}} | Error |
3*((x + y*I)+ \[Lambda]-x + \[Lambda])/((x + y*I)+ \[Lambda]-p + \[Lambda])*(EllipticPi[((x + y*I)+ \[Lambda]-p + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ 3*((x + y*I)+ \[Mu]-x + \[Mu])/((x + y*I)+ \[Mu]-p + \[Mu])*(EllipticPi[((x + y*I)+ \[Mu]-p + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu]),ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]-EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])])/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]] == 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x]- 3*1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] |
Missing Macro Error | Failure | - | Failed [300 / 300] {Complex[6.482970499990588, -0.8807575715831795] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[7.020988185402777, -1.8389880807014276] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</code
|
| 19.26#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = p(p+\lambda)(p+\mu)} | gamma = p*(p + lambda)*(p + mu) |
\[Gamma] == p*(p + \[Lambda])*(p + \[Mu]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = (p-x)(p-y)(p-z)} | delta = (p - x)*(p - y)*(p -(x + y*I)) |
\[Delta] == (p - x)*(p - y)*(p -(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x+\lambda}{y+\lambda}+\CarlsonellintRC@{x+\mu}{y+\mu} = \CarlsonellintRC@{x}{y}} | Error |
1/Sqrt[y + \[Lambda]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])]+ 1/Sqrt[y + \[Mu]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Mu])/(y + \[Mu])] == 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[1.7722794006718585, -0.740880873447254] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.579678795390187, -0.7154745309495683] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+\mu = \lambda^{-2}(\sqrt{x+\lambda}y+\sqrt{x}(y+\lambda))^{2}} | x + mu = (lambda)^(- 2)*(sqrt(x + lambda)*y +sqrt(x)*(y + lambda))^(2) |
x + \[Mu] == \[Lambda]^(- 2)*(Sqrt[x + \[Lambda]]*y +Sqrt[x]*(y + \[Lambda]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y+\mu = (y(y+\lambda)/\lambda^{2})(\sqrt{x}+\sqrt{x+\lambda})^{2}} | y + mu = (y*(y + lambda)/ (lambda)^(2))*(sqrt(x)+sqrt(x + lambda))^(2) |
y + \[Mu] == (y*(y + \[Lambda])/ \[Lambda]^(2))*(Sqrt[x]+Sqrt[x + \[Lambda]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{\alpha^{2}}{\alpha^{2}-\theta}+\CarlsonellintRC@{\beta^{2}}{\beta^{2}-\theta} = \CarlsonellintRC@{\sigma^{2}}{\sigma^{2}-\theta}} | Error |
1/Sqrt[\[Alpha]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Alpha]^(2)- \[Theta])]+ 1/Sqrt[\[Beta]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta]^(2))/(\[Beta]^(2)- \[Theta])] == 1/Sqrt[\[Sigma]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Sigma]^(2))/(\[Sigma]^(2)- \[Theta])] |
Missing Macro Error | Aborted | - | Successful [Tested: 2] |
| 19.26.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-y)\CarlsonellintRC@{x}{p}+(q-y)\CarlsonellintRC@{x}{q} = (\eta-\xi)\CarlsonellintRC@{\xi}{\eta}} | Error |
(p - y)* 1/Sqrt[p]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(p)]+(q - y)* 1/Sqrt[q]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(q)] == (\[Eta]- \[Xi])* 1/Sqrt[\[Eta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Xi])/(\[Eta])] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-3.0971074607887266, 1.6817857583573725] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-x)(q-x) = (y-x)^{2}} | (p - x)*(q - x) = (y - x)^(2) |
(p - x)*(q - x) == (y - x)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = y^{2}/x} | xi = (y)^(2)/ x |
\[Xi] == (y)^(2)/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = pq/x} | eta = p*q/ x |
\[Eta] == p*q/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta-\xi = p+q-2y} | eta - xi = p + q - 2*y |
\[Eta]- \[Xi] == p + q - 2*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{\lambda}{y+\lambda}{z+\lambda} = {\CarlsonsymellintRF@{0}{y}{z}-\CarlsonsymellintRF@{\mu}{y+\mu}{z+\mu},}} | 0.5*int(1/(sqrt(t+lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)- 0.5*int(1/(sqrt(t+mu)*sqrt(t+y + mu)*sqrt(t+(x + y*I)+ mu)), t = 0..infinity), |
EllipticF[ArcCos[Sqrt[\[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-\[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-\[Lambda]] == EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]- EllipticF[ArcCos[Sqrt[\[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-\[Mu])]/Sqrt[(x + y*I)+ \[Mu]-\[Mu]], |
Error | Failure | - | Error |
| 19.26.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\alpha}\CarlsonellintRC@{\beta}{\alpha+\beta}+\sqrt{\beta}\CarlsonellintRC@{\alpha}{\alpha+\beta} = \pi/2} | Error |
Sqrt[\[Alpha]]*1/Sqrt[\[Alpha]+ \[Beta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta])/(\[Alpha]+ \[Beta])]+Sqrt[\[Beta]]*1/Sqrt[\[Alpha]+ \[Beta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha])/(\[Alpha]+ \[Beta])] == Pi/ 2 |
Missing Macro Error | Failure | - | Successful [Tested: 9] |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = 2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == 2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]] |
Aborted | Failure | Skipped - Because timed out | Failed [180 / 180]
{Complex[-0.6992255245511445, 1.8246422705609677] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.7332476531334464, -0.3074481161267689] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda} = \CarlsonsymellintRF@{\frac{x+\lambda}{4}}{\frac{y+\lambda}{4}}{\frac{z+\lambda}{4}}} | 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) = 0.5*int(1/(sqrt(t+(x + lambda)/(4))*sqrt(t+(y + lambda)/(4))*sqrt(t+((x + y*I)+ lambda)/(4))), t = 0..infinity) |
2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]] == EllipticF[ArcCos[Sqrt[Divide[x + \[Lambda],4]/Divide[(x + y*I)+ \[Lambda],4]]],(Divide[(x + y*I)+ \[Lambda],4]-Divide[y + \[Lambda],4])/(Divide[(x + y*I)+ \[Lambda],4]-Divide[x + \[Lambda],4])]/Sqrt[Divide[(x + y*I)+ \[Lambda],4]-Divide[x + \[Lambda],4]] |
Failure | Failure | Skipped - Because timed out | Failed [180 / 180]
{Complex[-1.1343270456997319, -2.101834604175173] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.07907692856233961, -0.3004487668798371] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \sqrt{x}\sqrt{y}+\sqrt{y}\sqrt{z}+\sqrt{z}\sqrt{x}} | lambda = sqrt(x)*sqrt(y)+sqrt(y)*sqrt(x + y*I)+sqrt(x + y*I)*sqrt(x) |
\[Lambda] == Sqrt[x]*Sqrt[y]+Sqrt[y]*Sqrt[x + y*I]+Sqrt[x + y*I]*Sqrt[x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{y}{z} = 2\CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\frac{3}{\sqrt{z}(z+\lambda)}} | Error |
3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 2*3*(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/(((x + y*I)+ \[Lambda]-y + \[Lambda])*((x + y*I)+ \[Lambda]-x + \[Lambda])^(1/2))+Divide[3,Sqrt[x + y*I]*((x + y*I)+ \[Lambda])] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[0.4984590390126629, -1.2092907867192135] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.5295690158190058, -2.8195127867822802] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x}{y}{z} = 4\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}-\lambda\CarlsonsymellintRF@{x}{y}{z}-\sqrt{x}-\sqrt{y}-\sqrt{z}} | Error |
2*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == 4*Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]*(EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]^2])- \[Lambda]*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]-Sqrt[x]-Sqrt[y]-Sqrt[x + y*I] |
Missing Macro Error | Aborted | - | Failed [180 / 180] {Plus[Complex[2.330530943809637, 0.9206144902290859], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[-4.184639587172815, 1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[2.3171140130573056, 0.42755423781462054], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Tim
|
| 19.26.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{p} = 2\CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+3\CarlsonellintRC@{\alpha^{2}}{\beta^{2}}} | Error |
3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == 2*3*((x + y*I)+ \[Lambda]-x + \[Lambda])/((x + y*I)+ \[Lambda]-p + \[Lambda])*(EllipticPi[((x + y*I)+ \[Lambda]-p + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ 3*1/Sqrt[\[Beta]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Beta]^(2))] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = p(\sqrt{x}+\sqrt{y}+\sqrt{z})+\sqrt{x}\sqrt{y}\sqrt{z}} | alpha = p*(sqrt(x)+sqrt(y)+sqrt(x + y*I))+sqrt(x)*sqrt(y)*sqrt(x + y*I) |
\[Alpha] == p*(Sqrt[x]+Sqrt[y]+Sqrt[x + y*I])+Sqrt[x]*Sqrt[y]*Sqrt[x + y*I] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \sqrt{p}(p+\lambda)} | beta = sqrt(p)*(p + lambda) |
\[Beta] == Sqrt[p]*(p + \[Lambda]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta+\alpha = (\sqrt{p}+\sqrt{x})(\sqrt{p}+\sqrt{y})(\sqrt{p}+\sqrt{z})} | beta + alpha = (sqrt(p)+sqrt(x))*(sqrt(p)+sqrt(y))*(sqrt(p)+sqrt(x + y*I)) |
\[Beta]+ \[Alpha] == (Sqrt[p]+Sqrt[x])*(Sqrt[p]+Sqrt[y])*(Sqrt[p]+Sqrt[x + y*I]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta^{2}-\alpha^{2} = (p-x)(p-y)(p-z)} | (beta)^(2)- (alpha)^(2) = (p - x)*(p - y)*(p -(x + y*I)) |
\[Beta]^(2)- \[Alpha]^(2) == (p - x)*(p - y)*(p -(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = (\xi\zeta+\eta\zeta-\xi\eta)^{2}/(4\xi\eta\zeta)} | z = (xi*zeta + eta*zeta - xi*eta)^(2)/(4*xi*eta*zeta) |
z == (\[Xi]*\[Zeta]+ \[Eta]*\[Zeta]- \[Xi]*\[Eta])^(2)/(4*\[Xi]*\[Eta]*\[Zeta]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = 2\CarlsonellintRC@{x+\lambda}{y+\lambda}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == 2*1/Sqrt[y + \[Lambda]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])] |
Missing Macro Error | Failure | - | Failed [1 / 1]
{Indeterminate <- {Rule[x, 0.5], Rule[y, 0.5], Rule[λ, 1.5]} |
| 19.26.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}} | Error |
1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)] |
Missing Macro Error | Aborted | - | Failed [3 / 3]
{Indeterminate <- {Rule[a, 1.5], Rule[x, 1.5], Rule[y, 1.5]}Indeterminate <- {Rule[a, 0.5], Rule[x, 0.5], Rule[y, 0.5]} |
| 19.26.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{x^{2}-\theta} = 2\CarlsonellintRC@{s^{2}}{s^{2}-\theta}} | Error |
1/Sqrt[(x)^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((x)^(2)- \[Theta])] == 2*1/Sqrt[(s)^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-((s)^(2))/((s)^(2)- \[Theta])] |
Missing Macro Error | Failure | - | Successful [Tested: 2] |
| 19.27#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}(x+y)} | a = (1)/(2)*(x + y) |
a == Divide[1,2]*(x + y) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b = \tfrac{1}{2}(y+z)} | b = (1)/(2)*(y +(x + y*I)) |
b == Divide[1,2]*(y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \tfrac{1}{3}(x+y+z)} | c = (1)/(3)*(x + y +(x + y*I)) |
c == Divide[1,3]*(x + y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = (xyz)^{1/3}} | f = (x*y*(x + y*I))^(1/ 3) |
f == (x*y*(x + y*I))^(1/ 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g = (xy)^{1/2}} | g = (x*y)^(1/ 2) |
g == (x*y)^(1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h = (yz)^{1/2}} | h = (y*(x + y*I))^(1/ 2) |
h == (y*(x + y*I))^(1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | int((t)^(sigma - 1)* 0.5*int(1/(sqrt(t+0)*sqrt(t+t)*sqrt(t+1)), t = 0..infinity), t = 0..1) = (1)/(2)*(Beta(sigma, (1)/(2)))^(2) |
Integrate[(t)^(\[Sigma]- 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]/Sqrt[1-0], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Failure | Aborted | Failed [10 / 10] 10/10]: [[Float(undefined)+1.162857938*I <- {sigma = 1/2*3^(1/2)+1/2*I}Float(undefined)+.9984297790*I <- {sigma = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 19.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | Error |
Integrate[(t)^(\[Sigma]- 1)* Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]), {t, 0, 1}, GenerateConditions->None] == Divide[\[Sigma],4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | Error |
Integrate[(t)^(\[Sigma]- 1)*(1 - t)* 3*(EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)])/((1-t)*(1-0)^(1/2)), {t, 0, 1}, GenerateConditions->None] == Divide[3,4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}\CarlsonsymellintRD@{x}{y}{t}\diff{t} = 6\CarlsonsymellintRF@{x}{y}{z}} | Error |
Integrate[3*(EllipticF[ArcCos[Sqrt[x/t]],(t-y)/(t-x)]-EllipticE[ArcCos[Sqrt[x/t]],(t-y)/(t-x)])/((t-y)*(t-x)^(1/2)), {t, (x + y*I), Infinity}, GenerateConditions->None] == 6*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\CarlsonsymellintRD@{x}{y}{v^{2}z+(1-v^{2})p}\diff{v} = \CarlsonsymellintRJ@{x}{y}{z}{p}} | Error |
Integrate[3*(EllipticF[ArcCos[Sqrt[x/(v)^(2)*(x + y*I)+(1 - (v)^(2))* p]],((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)/((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)]-EllipticE[ArcCos[Sqrt[x/(v)^(2)*(x + y*I)+(1 - (v)^(2))* p]],((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)/((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)])/(((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)*((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)^(1/2)), {v, 0, 1}, GenerateConditions->None] == 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRJ@{x}{y}{z}{r^{2}}\diff{r} = \tfrac{3}{2}\pi\CarlsonsymellintRF@{xy}{xz}{yz}} | Error |
Integrate[3*(x + y*I-x)/(x + y*I-(r)^(2))*(EllipticPi[(x + y*I-(r)^(2))/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x], {r, 0, Infinity}, GenerateConditions->None] == Divide[3,2]*Pi*EllipticF[ArcCos[Sqrt[x*y/y*(x + y*I)]],(y*(x + y*I)-x*(x + y*I))/(y*(x + y*I)-x*y)]/Sqrt[y*(x + y*I)-x*y] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRJ@{tx}{y}{z}{tp}\diff{t} = \frac{6}{\sqrt{p}}\CarlsonellintRC@{p}{x}\CarlsonsymellintRF@{0}{y}{z}} | Error |
Integrate[3*(x + y*I-t*x)/(x + y*I-t*p)*(EllipticPi[(x + y*I-t*p)/(x + y*I-t*x),ArcCos[Sqrt[t*x/x + y*I]],(x + y*I-y)/(x + y*I-t*x)]-EllipticF[ArcCos[Sqrt[t*x/x + y*I]],(x + y*I-y)/(x + y*I-t*x)])/Sqrt[x + y*I-t*x], {t, 0, Infinity}, GenerateConditions->None] == Divide[6,Sqrt[p]]*1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(p)/(x)]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}\CarlsonsymellintRF@{\sin^{2}@@{\theta}\cos^{2}@{x+y}}{\sin^{2}@@{\theta}\cos^{2}@{x-y}}{1}\diff{\theta} = \CarlsonsymellintRF@{0}{\cos^{2}@@{x}}{1}\CarlsonsymellintRF@{0}{\cos^{2}@@{y}}{1}} | int(0.5*int(1/(sqrt(t+(sin(theta))^(2)* (cos(x + y))^(2))*sqrt(t+(sin(theta))^(2)* (cos(x - y))^(2))*sqrt(t+1)), t = 0..infinity), theta = 0..Pi/ 2) = 0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(x))^(2))*sqrt(t+1)), t = 0..infinity)*0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(y))^(2))*sqrt(t+1)), t = 0..infinity) |
Integrate[EllipticF[ArcCos[Sqrt[(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)/1]],(1-(Sin[\[Theta]])^(2)* (Cos[x - y])^(2))/(1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2))]/Sqrt[1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[x])^(2))/(1-0)]/Sqrt[1-0]*EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[y])^(2))/(1-0)]/Sqrt[1-0] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRF@{(ac+bd)^{2}}{(ad+bc)^{2}}{4abcd\cosh^{2}@@{z}}\diff{z} = \tfrac{1}{2}\CarlsonsymellintRF@{0}{a^{2}}{b^{2}}\CarlsonsymellintRF@{0}{c^{2}}{d^{2}}} | int(0.5*int(1/(sqrt(t+(a*c + b*d)^(2))*sqrt(t+(a*d + b*c)^(2))*sqrt(t+4*a*b*c*d*(cosh(z))^(2))), t = 0..infinity), z = 0..infinity) = (1)/(2)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a)^(2))*sqrt(t+(b)^(2))), t = 0..infinity)*0.5*int(1/(sqrt(t+0)*sqrt(t+(c)^(2))*sqrt(t+(d)^(2))), t = 0..infinity) |
Integrate[EllipticF[ArcCos[Sqrt[(a*c + b*d)^(2)/4*a*b*c*d*(Cosh[z])^(2)]],(4*a*b*c*d*(Cosh[z])^(2)-(a*d + b*c)^(2))/(4*a*b*c*d*(Cosh[z])^(2)-(a*c + b*d)^(2))]/Sqrt[4*a*b*c*d*(Cosh[z])^(2)-(a*c + b*d)^(2)], {z, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]/Sqrt[(b)^(2)-0]*EllipticF[ArcCos[Sqrt[0/(d)^(2)]],((d)^(2)-(c)^(2))/((d)^(2)-0)]/Sqrt[(d)^(2)-0] |
Error | Aborted | - | Skipped - Because timed out |
| 19.29#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle X_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}x}} | X[alpha] = sqrt(a[alpha]+ b[alpha]*x) |
Subscript[X, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Y_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}y}} | Y[alpha] = sqrt(a[alpha]+ b[alpha]*y) |
Subscript[Y, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*y] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{\alpha\beta} = a_{\alpha}b_{\beta}-a_{\beta}b_{\alpha}} | d[alpha*beta] = a[alpha]*b[beta]- a[beta]*b[alpha] |
Subscript[d, \[Alpha]*\[Beta]] == Subscript[a, \[Alpha]]*Subscript[b, \[Beta]]- Subscript[a, \[Beta]]*Subscript[b, \[Alpha]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(t) = \prod_{\alpha=1}^{4}\sqrt{a_{\alpha}+b_{\alpha}t}} | s*(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..4) |
s*(t) == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 4}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{s(t)} = 2\CarlsonsymellintRF@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}} | 0.5*int(1/(sqrt(t+U(U[12])^(2))*sqrt(t+U(U[13])^(2))*sqrt(t+U(U[23])^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))]/Sqrt[U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = (X_{\alpha}X_{\beta}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}X_{\gamma}X_{\delta})/(x-y)} | U[alpha*beta] = (X[alpha]*X[beta]*Y[gamma]*Y[delta]+ Y[alpha]*Y[beta]*X[gamma]*X[delta])/(x - y) |
Subscript[U, \[Alpha]*\[Beta]] == (Subscript[X, \[Alpha]]*Subscript[X, \[Beta]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]*Subscript[Y, \[Beta]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]])/(x - y) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = U_{\beta\alpha}} | U[alpha*beta] = U[beta*alpha] |
Subscript[U, \[Alpha]*\[Beta]] == Subscript[U, \[Beta]*\[Alpha]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta}^{2}-U_{\alpha\gamma}^{2} = d_{\alpha\delta}d_{\beta\gamma}} | (U[alpha*beta])^(2)- (U[alpha*gamma])^(2) = d[alpha*delta]*d[beta*gamma] |
(Subscript[U, \[Alpha]*\[Beta]])^(2)- (Subscript[U, \[Alpha]*\[Gamma]])^(2) == Subscript[d, \[Alpha]*\[Delta]]*Subscript[d, \[Beta]*\[Gamma]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = \sqrt{b_{\alpha}}\sqrt{b_{\beta}}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}\sqrt{b_{\gamma}}\sqrt{b_{\delta}},} | U[alpha*beta] = sqrt(b[alpha])*sqrt(b[beta])*Y[gamma]*Y[delta]+ Y[alpha]*Y[beta]*sqrt(b[gamma])*sqrt(b[delta]), |
Subscript[U, \[Alpha]*\[Beta]] == Sqrt[Subscript[b, \[Alpha]]]*Sqrt[Subscript[b, \[Beta]]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]*Subscript[Y, \[Beta]]*Sqrt[Subscript[b, \[Gamma]]]*Sqrt[Subscript[b, \[Delta]]], |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = X_{\alpha}X_{\beta}\sqrt{-b_{\gamma}}\sqrt{-b_{\delta}}+\sqrt{-b_{\alpha}}\sqrt{-b_{\beta}}X_{\gamma}X_{\delta}} | U[alpha*beta] = X[alpha]*X[beta]*sqrt(- b[gamma])*sqrt(- b[delta])+sqrt(- b[alpha])*sqrt(- b[beta])*X[gamma]*X[delta] |
Subscript[U, \[Alpha]*\[Beta]] == Subscript[X, \[Alpha]]*Subscript[X, \[Beta]]*Sqrt[- Subscript[b, \[Gamma]]]*Sqrt[- Subscript[b, \[Delta]]]+Sqrt[- Subscript[b, \[Alpha]]]*Sqrt[- Subscript[b, \[Beta]]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{\delta}+b_{\delta}t}\frac{\diff{t}}{s(t)} = \tfrac{2}{3}d_{\alpha\beta}d_{\alpha\gamma}\CarlsonsymellintRD@{U_{\alpha\beta}^{2}}{U_{\alpha\gamma}^{2}}{U_{\alpha\delta}^{2}}+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha\delta}}} | Error |
Integrate[Divide[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t,Subscript[a, \[Delta]]+ Subscript[b, \[Delta]]*t]*Divide[1,s*(t)], {t, y, x}, GenerateConditions->None] == 3*(EllipticF[ArcCos[Sqrt[U(Subscript[U, \[Alpha]*\[Beta]])^(2)/U(Subscript[U, \[Alpha]*\[Delta]])^(2)]],(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))/(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))]-EllipticE[ArcCos[Sqrt[U(Subscript[U, \[Alpha]*\[Beta]])^(2)/U(Subscript[U, \[Alpha]*\[Delta]])^(2)]],(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))/(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))])/((U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))*(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))^(1/2))+Divide[2*Subscript[X, \[Alpha]]*Subscript[Y, \[Alpha]],Subscript[X, \[Delta]]*Subscript[Y, \[Delta]]*Subscript[U, \[Alpha]*\[Delta]]] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{5}+b_{5}t}\frac{\diff{t}}{s(t)} = \frac{2}{3}\frac{d_{\alpha\beta}d_{\alpha\gamma}d_{\alpha\delta}}{d_{\alpha 5}}\CarlsonsymellintRJ@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}{U_{\alpha 5}^{2}}+2\CarlsonellintRC@{S_{\alpha 5}^{2}}{Q_{\alpha 5}^{2}}} | Error |
3*(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, \[Alpha]*5])^(2))*(EllipticPi[(U(Subscript[U, 23])^(2)-U(Subscript[U, \[Alpha]*5])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)),ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))]-EllipticF[ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))])/Sqrt[U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)]1/Sqrt[Q(Subscript[Q, \[Alpha]*5])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(S(Subscript[S, \[Alpha]*5])^(2))/(Q(Subscript[Q, \[Alpha]*5])^(2))] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha 5}^{2} = U_{\alpha\beta}^{2}-\frac{d_{\alpha\gamma}d_{\alpha\delta}d_{\beta 5}}{d_{\alpha 5}}} | (U[alpha*5])^(2) = (U[alpha*beta])^(2)-(d[alpha*gamma]*d[alpha*delta]*d[beta*5])/(d[alpha*5]) |
(Subscript[U, \[Alpha]*5])^(2) == (Subscript[U, \[Alpha]*\[Beta]])^(2)-Divide[Subscript[d, \[Alpha]*\[Gamma]]*Subscript[d, \[Alpha]*\[Delta]]*Subscript[d, \[Beta]*5],Subscript[d, \[Alpha]*5]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{\alpha 5} = \frac{1}{x-y}\left(\frac{X_{\beta}X_{\gamma}X_{\delta}}{X_{\alpha}}Y_{5}^{2}+\frac{Y_{\beta}Y_{\gamma}Y_{\delta}}{Y_{\alpha}}X_{5}^{2}\right)} | S[alpha*5] ((X[beta]*X[gamma]*X[delta])/(X[alpha])*Y(Y[5])^(2)+(Y[beta]*Y[gamma]*Y[delta])/(Y[alpha])*X(X[5])^(2)) |
Subscript[S, \[Alpha]*5] (Divide[Subscript[X, \[Beta]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]],Subscript[X, \[Alpha]]]*Y(Subscript[Y, 5])^(2)+Divide[Subscript[Y, \[Beta]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]],Subscript[Y, \[Alpha]]]*X(Subscript[X, 5])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{\alpha 5} = \frac{X_{5}Y_{5}}{X_{\alpha}Y_{\alpha}}U_{\alpha 5}} | Q[alpha*5] = (X[5]*Y[5])/(X[alpha]*Y[alpha])*U[alpha*5] |
Subscript[Q, \[Alpha]*5] == Divide[Subscript[X, 5]*Subscript[Y, 5],Subscript[X, \[Alpha]]*Subscript[Y, \[Alpha]]]*Subscript[U, \[Alpha]*5] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{\alpha 5}^{2}-Q_{\alpha 5}^{2} = \frac{d_{\beta 5}d_{\gamma 5}d_{\delta 5}}{d_{\alpha 5}}} | (S[alpha*5])^(2)- (Q[alpha*5])^(2) = (d[beta*5]*d[gamma*5]*d[delta*5])/(d[alpha*5]) |
(Subscript[S, \[Alpha]*5])^(2)- (Subscript[Q, \[Alpha]*5])^(2) == Divide[Subscript[d, \[Beta]*5]*Subscript[d, \[Gamma]*5]*Subscript[d, \[Delta]*5],Subscript[d, \[Alpha]*5]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u}^{b}\sqrt{\frac{a-t}{(b-t)(t-c)^{3}}}\diff{t} = -\tfrac{2}{3}{(a-b)}{(b-u)}^{3/2}\CarlsonsymellintRD@@{(a-b)(u-c)}{(b-c)(a-u)}{(a-b)(b-c)}+\frac{2}{b-c}\sqrt{\frac{(a-u)(b-u)}{u-c}}} | Error |
Integrate[Sqrt[Divide[a - t,(b - t)*(t - c)^(3)]], {t, u, b}, GenerateConditions->None] == -Divide[2,3]*(a - b)*(b - u)^(3/ 2)* 3*(EllipticF[ArcCos[Sqrt[(a - b)*(u - c)/(a - b)*(b - c)]],((a - b)*(b - c)-(b - c)*(a - u))/((a - b)*(b - c)-(a - b)*(u - c))]-EllipticE[ArcCos[Sqrt[(a - b)*(u - c)/(a - b)*(b - c)]],((a - b)*(b - c)-(b - c)*(a - u))/((a - b)*(b - c)-(a - b)*(u - c))])/(((a - b)*(b - c)-(b - c)*(a - u))*((a - b)*(b - c)-(a - b)*(u - c))^(1/2))+Divide[2,b - c]*Sqrt[Divide[(a - u)*(b - u),u - c]] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{m}) = \int_{y}^{x}\prod_{\alpha=1}^{h}(a_{\alpha}+b_{\alpha}t)^{-1/2}\prod_{j=1}^{n}(a_{j}+b_{j}t)^{m_{j}}\diff{t}} | I*(m) = int(product((a[alpha]+ b[alpha]*t)^(- 1/ 2)* product((a[j]+ b[j]*t)^(m[j]), j = 1..n), alpha = 1..h), t = y..x) |
I*(m) == Integrate[Product[(Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t)^(- 1/ 2)* Product[(Subscript[a, j]+ Subscript[b, j]*t)^(Subscript[m, j]), {j, 1, n}, GenerateConditions->None], {\[Alpha], 1, h}, GenerateConditions->None], {t, y, x}, GenerateConditions->None] |
Aborted | Aborted | Error | Skipped - Because timed out |
| 19.29.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{j}I(\mathbf{e}_{l}-\mathbf{e}_{j}) = d_{lj}I(-\mathbf{e}_{j})+b_{l}I(\boldsymbol{{0}})} | b[j]*I*(e[l]- e[j]) = d[l*j]*I*(- e[j])+ b[l]*I*(0) |
Subscript[b, j]*I*(Subscript[e, l]- Subscript[e, j]) == Subscript[d, l*j]*I*(- Subscript[e, j])+ Subscript[b, l]*I*(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{\beta}b_{\gamma}I(\mathbf{e}_{\alpha}) = d_{\alpha\beta}d_{\alpha\gamma}I(-\mathbf{e}_{\alpha})+2b_{\alpha}\left(\frac{s(x)}{a_{\alpha}+b_{\alpha}x}-\frac{s(y)}{a_{\alpha}+b_{\alpha}y}\right)} | b[beta]*b[gamma]*I*(e[alpha]) = d[alpha*beta]*d[alpha*gamma]*I*(- e[alpha])+ 2*b[alpha]*((s*(x))/(a[alpha]+ b[alpha]*x)-(s*(y))/(a[alpha]+ b[alpha]*y)) |
Subscript[b, \[Beta]]*Subscript[b, \[Gamma]]*I*(Subscript[e, \[Alpha]]) == Subscript[d, \[Alpha]*\[Beta]]*Subscript[d, \[Alpha]*\[Gamma]]*I*(- Subscript[e, \[Alpha]])+ 2*Subscript[b, \[Alpha]]*(Divide[s*(x),Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*x]-Divide[s*(y),Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*y]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(t) = \prod_{\alpha=1}^{3}\sqrt{a_{\alpha}+b_{\alpha}t}} | s*(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..3) |
s*(t) == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 3}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{j}^{q}I(q\mathbf{e}_{l}) = \sum_{r=0}^{q}\binom{q}{r}b_{l}^{r}d_{lj}^{q-r}I(r\mathbf{e}_{j})} | (b[j])^(q)*I*sum(binomial(q,r)*b(b[l])^(r)*d(d[l*j])^(q - r)*I*(r*e[j]), r = 0..q) |
(Subscript[b, j])^(q)*I*Sum[Binomial[q,r]*b(Subscript[b, l])^(r)*d(Subscript[d, l*j])^(q - r)*I*(r*Subscript[e, j]), {r, 0, q}, GenerateConditions->None] |
Failure | Failure | Error | Skipped - Because timed out |
| 19.29.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \CarlsonsymellintRF@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x) = 0.5*int(1/(sqrt(t+(U)^(2)+ a[1]*b[2])*sqrt(t+(U)^(2)+ a[2]*b[1])*sqrt(t+(U)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]/Sqrt[(U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]] |
Aborted | Aborted | Manual Skip! | Skipped - Because timed out |
| 19.29.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{t^{2}\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}a_{1}a_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xy/U)} | Error |
Integrate[Divide[(t)^(2),Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == Divide[1,3]*Subscript[a, 1]*Subscript[a, 2]*3*(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])*((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])^(1/2))+(x*y/ U) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{t^{2}\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}b_{1}b_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xyU)^{-1}} | Error |
Integrate[Divide[1,(t)^(2)*Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == Divide[1,3]*Subscript[b, 1]*Subscript[b, 2]*3*(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])*((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])^(1/2))+(x*y*U)^(- 1) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x^{2}-y^{2})U = x\sqrt{Q_{1}(y)Q_{2}(y)}+y\sqrt{Q_{1}(x)Q_{2}(x)}} | ((x)^(2)- (y)^(2))* U = x*sqrt(Q[1]*(y)* Q[2]*(y))+ y*sqrt(Q[1]*(x)* Q[2]*(x)) |
((x)^(2)- (y)^(2))* U == x*Sqrt[Subscript[Q, 1]*(y)* Subscript[Q, 2]*(y)]+ y*Sqrt[Subscript[Q, 1]*(x)* Subscript[Q, 2]*(x)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+a^{2})(t^{2}-b^{2})}} = \CarlsonsymellintRF@{y^{2}+a^{2}}{y^{2}-b^{2}}{y^{2}}} | int((1)/(sqrt(((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2)))), t = y..infinity) = 0.5*int(1/(sqrt(t+(y)^(2)+ (a)^(2))*sqrt(t+(y)^(2)- (b)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2))]], {t, y, Infinity}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(y)^(2)+ (a)^(2)/(y)^(2)]],((y)^(2)-(y)^(2)- (b)^(2))/((y)^(2)-(y)^(2)+ (a)^(2))]/Sqrt[(y)^(2)-(y)^(2)+ (a)^(2)] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = 4\CarlsonsymellintRF@{U}{U+D_{12}+V}{U+D_{12}-V}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x) = 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U + D[12]+ V)*sqrt(t+U + D[12]- V)), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == 4*EllipticF[ArcCos[Sqrt[U/U + Subscript[D, 12]- V]],(U + Subscript[D, 12]- V-U + Subscript[D, 12]+ V)/(U + Subscript[D, 12]- V-U)]/Sqrt[U + Subscript[D, 12]- V-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = S_{1}S_{2}} | (x - y)^(2)* U = S[1]*S[2] |
(x - y)^(2)* U == Subscript[S, 1]*Subscript[S, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{j} = \left(\sqrt{Q_{j}(x)}+\sqrt{Q_{j}(y)}\right)^{2}-h_{j}(x-y)^{2}} | S[j] = (sqrt(Q[j]*(x))+sqrt(Q[j]*(y)))^(2)- h[j]*(x - y)^(2) |
Subscript[S, j] == (Sqrt[Subscript[Q, j]*(x)]+Sqrt[Subscript[Q, j]*(y)])^(2)- Subscript[h, j]*(x - y)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{jl} = 2f_{j}h_{l}+2h_{j}f_{l}-g_{j}g_{l}} | D[j*l] = 2*f[j]*h[l]+ 2*h[j]*f[l]- g[j]*g[l] |
Subscript[D, j*l] == 2*Subscript[f, j]*Subscript[h, l]+ 2*Subscript[h, j]*Subscript[f, l]- Subscript[g, j]*Subscript[g, l] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V = \sqrt{D_{12}^{2}-D_{11}D_{22}}} | V sqrt(D(D[12])^(2)- D[11]*D[22]) |
V Sqrt[D(Subscript[D, 12])^(2)- Subscript[D, 11]*Subscript[D, 22]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1} = (X_{1}Y_{2}+Y_{1}X_{2})^{2}} | S[1] = (X[1]*Y[2]+ Y[1]*X[2])^(2) |
Subscript[S, 1] == (Subscript[X, 1]*Subscript[Y, 2]+ Subscript[Y, 1]*Subscript[X, 2])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle X_{j} = \sqrt{a_{j}+b_{j}x}} | X[j] = sqrt(a[j]+ b[j]*x) |
Subscript[X, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Y_{j} = \sqrt{a_{j}+b_{j}y}} | Y[j] = sqrt(a[j]+ b[j]*y) |
Subscript[Y, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*y] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{12} = 2a_{1}a_{2}h_{2}+2b_{1}b_{2}f_{2}-(a_{1}b_{2}+a_{2}b_{1})g_{2}} | D[12] = 2*a[1]*a[2]*h[2]+ 2*b[1]*b[2]*f[2]-(a[1]*b[2]+ a[2]*b[1])* g[2] |
Subscript[D, 12] == 2*Subscript[a, 1]*Subscript[a, 2]*Subscript[h, 2]+ 2*Subscript[b, 1]*Subscript[b, 2]*Subscript[f, 2]-(Subscript[a, 1]*Subscript[b, 2]+ Subscript[a, 2]*Subscript[b, 1])* Subscript[g, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{11} = -(a_{1}b_{2}-a_{2}b_{1})^{2}} | D[11] = -(a[1]*b[2]- a[2]*b[1])^(2) |
Subscript[D, 11] == -(Subscript[a, 1]*Subscript[b, 2]- Subscript[a, 2]*Subscript[b, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1} = (X_{1}+Y_{1})^{2}} | S[1] = (X[1]+ Y[1])^(2) |
Subscript[S, 1] == (Subscript[X, 1]+ Subscript[Y, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{12} = 2a_{1}h_{2}-b_{1}g_{2}} | D[12] = 2*a[1]*h[2]- b[1]*g[2] |
Subscript[D, 12] == 2*Subscript[a, 1]*Subscript[h, 2]- Subscript[b, 1]*Subscript[g, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{11} = -b_{1}^{2}} | D[11] = - (b[1])^(2) |
Subscript[D, 11] == - (Subscript[b, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{3}-a^{3}}} = 4\CarlsonsymellintRF@{U}{U-3a+2\sqrt{3}a}{U-3a-2\sqrt{3}a}} | int((1)/(sqrt((t)^(3)- (a)^(3))), t = y..x) = 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U - 3*a + 2*sqrt(3)*a)*sqrt(t+U - 3*a - 2*sqrt(3)*a)), t = 0..infinity) |
Integrate[Divide[1,Sqrt[(t)^(3)- (a)^(3)]], {t, y, x}, GenerateConditions->None] == 4*EllipticF[ArcCos[Sqrt[U/U - 3*a - 2*Sqrt[3]*a]],(U - 3*a - 2*Sqrt[3]*a-U - 3*a + 2*Sqrt[3]*a)/(U - 3*a - 2*Sqrt[3]*a-U)]/Sqrt[U - 3*a - 2*Sqrt[3]*a-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = (\sqrt{x-a}+\sqrt{y-a})^{2}\left((\xi+\eta)^{2}-(x-y)^{2}\right)} | (x - y)^(2)* U = (sqrt(x - a)+sqrt(y - a))^(2)*((xi + eta)^(2)-(x - y)^(2)) |
(x - y)^(2)* U == (Sqrt[x - a]+Sqrt[y - a])^(2)*((\[Xi]+ \[Eta])^(2)-(x - y)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = \sqrt{x^{2}+ax+a^{2}}} | xi = sqrt((x)^(2)+ a*x + (a)^(2)) |
\[Xi] == Sqrt[(x)^(2)+ a*x + (a)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = \sqrt{y^{2}+ay+a^{2}}} | eta = sqrt((y)^(2)+ a*y + (a)^(2)) |
\[Eta] == Sqrt[(y)^(2)+ a*y + (a)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q(t^{2})}} = 2\CarlsonsymellintRF@{U}{U-g+2\sqrt{fh}}{U-g-2\sqrt{fh}}} | int((1)/(sqrt(Q*((t)^(2)))), t = y..x) = 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U - g + 2*sqrt(f*h))*sqrt(t+U - g - 2*sqrt(f*h))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Q*((t)^(2))]], {t, y, x}, GenerateConditions->None] == 2*EllipticF[ArcCos[Sqrt[U/U - g - 2*Sqrt[f*h]]],(U - g - 2*Sqrt[f*h]-U - g + 2*Sqrt[f*h])/(U - g - 2*Sqrt[f*h]-U)]/Sqrt[U - g - 2*Sqrt[f*h]-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = \left(\sqrt{Q(x^{2})}+\sqrt{Q(y^{2})}\right)^{2}-h(x^{2}-y^{2})^{2}} | (x - y)^(2)* U = (sqrt(Q*((x)^(2)))+sqrt(Q*((y)^(2))))^(2)- h*((x)^(2)- (y)^(2))^(2) |
(x - y)^(2)* U == (Sqrt[Q*((x)^(2))]+Sqrt[Q*((y)^(2))])^(2)- h*((x)^(2)- (y)^(2))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{4}+a^{4}}} = 2\CarlsonsymellintRF@{U}{U+2a^{2}}{U-2a^{2}}} | int((1)/(sqrt((t)^(4)+ (a)^(4))), t = y..x) = 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U + 2*(a)^(2))*sqrt(t+U - 2*(a)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[(t)^(4)+ (a)^(4)]], {t, y, x}, GenerateConditions->None] == 2*EllipticF[ArcCos[Sqrt[U/U - 2*(a)^(2)]],(U - 2*(a)^(2)-U + 2*(a)^(2))/(U - 2*(a)^(2)-U)]/Sqrt[U - 2*(a)^(2)-U] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[0.06910876495694751, 1.480960979386122] <- {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[1.3051585498245286, 1.480960979386122] <- {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.29.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = \left(\sqrt{x^{4}+a^{4}}+\sqrt{y^{4}+a^{4}}\right)^{2}-(x^{2}-y^{2})^{2}} | (x - y)^(2)* U = (sqrt((x)^(4)+ (a)^(4))+sqrt((y)^(4)+ (a)^(4)))^(2)-((x)^(2)- (y)^(2))^(2) |
(x - y)^(2)* U == (Sqrt[(x)^(4)+ (a)^(4)]+Sqrt[(y)^(4)+ (a)^(4)])^(2)-((x)^(2)- (y)^(2))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\sin@@{\phi}} | x = a*sin(phi) |
x == a*Sin[\[Phi]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[2.788470502+.5063946946*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}1.788470502+.5063946946*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [180 / 180]
{Complex[2.1491827752870476, 0.34394646701016035] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.093555858156998, 0.6491787480429551] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\cos@@{\phi}} | y = b*cos(phi) |
y == b*Cos[\[Phi]] |
Failure | Failure | Failed [108 / 108] 108/108]: [[-1.393894198 <- {b = -3/2, phi = 3/2, y = -3/2}1.606105802 <- {b = -3/2, phi = 3/2, y = 3/2} |
Failed [108 / 108]
{-1.3938941974984456 <- {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 1.5]}-0.18362615716444086 <- {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 0.5]} |
| 19.30.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}} | s = a*int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi) |
s == a*Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.30.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s/a = \incellintEk@{\phi}{k}} | s/ a = EllipticE(sin(phi), k) |
s/ a == EllipticE[\[Phi], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.1410196655-.3375964631*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 1}-.36391978e-1+.5433649104e-1*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.5672114831419685, -0.22929764467344024] <- {Rule[a, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.5579190406370536, -0.16535187593702125] <- {Rule[a, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = {\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}}} | Error |
EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [180 / 180]
{Complex[3.5743811704478246, 0.7698502565730785] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[3.9424508382496875, -1.017653751864599] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = 1-(b^{2}/a^{2})} | (k)^(2) = 1 -((b)^(2)/ (a)^(2)) |
(k)^(2) == 1 -((b)^(2)/ (a)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \csc^{2}@@{\phi}} | c = (csc(phi))^(2) |
c == (Csc[\[Phi]])^(2) |
Failure | Failure | Failed [60 / 60] 60/60]: [[-2.359812877+.7993130071*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I}-1.296085040-.8173084059*I <- {c = -3/2, phi = -1/2+1/2*I*3^(1/2)} |
Failed [60 / 60]
{Complex[-3.841312467237177, 3.4490957612740374] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.17530792640393877, -3.4502399957777015] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 4a\compellintEk@{k}} | L*(a , b) = 4*a*EllipticE(k) |
L*(a , b) == 4*a*EllipticE[(k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[(.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+6.000000000 <- {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 1}(.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+2.437793319+8.063125386*I <- {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 2} |
Error |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4a\compellintEk@{k} = 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1}} | Error |
4*a*EllipticE[(k)^2] == 8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [108 / 108]
{12.849555921538759 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1]}Complex[16.411762602778996, -8.063125388322588] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1} = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}} | Error |
8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) == 8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [18 / 36]
{-37.69911184307752 <- {Rule[a, -1.5], Rule[b, -1.5]}-37.69911184307752 <- {Rule[a, -1.5], Rule[b, 1.5]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}} = 8ab\CarlsonsymellintRG@{0}{a^{-2}}{b^{-2}}} | Error |
8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) == 8*a*b*Sqrt[(b)^(- 2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(- 2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(- 2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(- 2)]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [18 / 36]
{37.69911184307752 <- {Rule[a, -1.5], Rule[b, 1.5]}26.729786441110512 <- {Rule[a, -1.5], Rule[b, 0.5]} |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{s}{(1/k)} = \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k}} | subs( temp=(1/ k), diff( s, temp$(1) ) ) = sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) |
(D[s, {temp, 1}]/.temp-> (1/ k)) == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] |
Failure | Failure | Successful [Tested: 300] | Failed [20 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, -2]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, 2]} |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k} = \sqrt{a^{2}-b^{2}}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) = sqrt((a)^(2)- (b)^(2))*0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1] |
Error | Failure | Skip - symbolical successful subtest | Skip - No test values generated |
| 19.30#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\sqrt{t+1}} | x = a*sqrt(t + 1) |
x == a*Sqrt[t + 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\sqrt{t}} | y = b*sqrt(t) |
y == b*Sqrt[t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\diff{t}} | s = (1)/(2)*int(sqrt((((a)^(2)+ (b)^(2))* t + (b)^(2))/(t*(t + 1))), t = 0..(y)^(2)/ (b)^(2)) |
s == Divide[1,2]*Integrate[Sqrt[Divide[((a)^(2)+ (b)^(2))* t + (b)^(2),t*(t + 1)]], {t, 0, (y)^(2)/ (b)^(2)}, GenerateConditions->None] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-3.149531120 <- {a = -3/2, b = -3/2, s = -3/2, y = -3/2}-3.149531120 <- {a = -3/2, b = -3/2, s = -3/2, y = 3/2} |
Skipped - Because timed out |
| 19.30.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \tfrac{1}{2}I(\mathbf{e}_{1})} | s = (1)/(2)*I*(e[1]) |
s == Divide[1,2]*I*(Subscript[e, 1]) |
Failure | Failure | Failed [298 / 300] 298/300]: [[-1.750000000-.4330127020*I <- {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = 1/2*3^(1/2)+1/2*I}-1.066987298-.2500000002*I <- {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = -1/2+1/2*I*3^(1/2)} |
Failed [180 / 180]
{Complex[-1.375, -0.21650635094610968] <- {Rule[Complex[0, 1], 1], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.375, -0.21650635094610968] <- {Rule[Complex[0, 1], 2], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}I(\mathbf{e}_{1}) = -\tfrac{1}{3}a^{2}b^{2}\CarlsonsymellintRD@{r}{r+b^{2}+a^{2}}{r+b^{2}}+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{2}}}} | Error |
Divide[1,2]*I*(Subscript[e, 1]) == -Divide[1,3]*(a)^(2)* (b)^(2)* 3*(EllipticF[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)]-EllipticE[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)])/((r + (b)^(2)-r + (b)^(2)+ (a)^(2))*(r + (b)^(2)-r)^(1/2))+ y*Sqrt[Divide[r + (b)^(2)+ (a)^(2),r + (b)^(2)]] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Skip - No test values generated |
| 19.30.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r^{2} = 2a^{2}\cos@{2\theta}} | (r)^(2) = 2*(a)^(2)* cos(2*theta) |
(r)^(2) == 2*(a)^(2)* Cos[2*\[Theta]] |
Failure | Failure | Failed [108 / 108] 108/108]: [[6.704966234 <- {a = -3/2, r = -3/2, theta = 3/2}-.181360376 <- {a = -3/2, r = -3/2, theta = 1/2} |
Failed [108 / 108]
{6.704966234702004 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 1.5]}-0.18136037640662916 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 0.5]} |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}}} | s = 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) |
s == 2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] |
Error | Failure | - | Failed [208 / 216]
{0.042085201578189846 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[s, -1.5]}3.04208520157819 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[s, 1.5]} |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}} = \sqrt{2a^{2}}\CarlsonsymellintRF@{q-1}{q}{q+1}} | 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) = sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+q - 1)*sqrt(t+q)*sqrt(t+q + 1)), t = 0..infinity) |
2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] == Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[q - 1/q + 1]],(q + 1-q)/(q + 1-q - 1)]/Sqrt[q + 1-q - 1] |
Error | Failure | - | Failed [12 / 12]
{Indeterminate <- {Rule[a, -1.5], Rule[q, 2], Rule[r, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[q, 2], Rule[r, 1.5]} |
| 19.30.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\incellintFk@{\phi}{1/\sqrt{2}}} | s = a*EllipticF(sin(phi), 1/(sqrt(2))) |
s == a*EllipticF[\[Phi], (1/(Sqrt[2]))^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.201379324+.8785912788*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2}2.798620676+.8785912788*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = 3/2} |
Failed [300 / 300]
{Complex[-0.8505476575870029, 0.390685462269601] <- {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.859414812385125, 0.6494166239344216] <- {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P = 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2}} | P = 4*sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity) |
P == 4*Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] |
Failure | Failure | Failed [60 / 60] 60/60]: [[-10.25842266+.5000000000*I <- {P = 1/2*3^(1/2)+1/2*I, a = -3/2}-10.25842266+.5000000000*I <- {P = 1/2*3^(1/2)+1/2*I, a = 3/2} |
Failed [60 / 60]
{Complex[-10.691435361916012, 0.24999999999999997] <- {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-11.37444806380823, 0.43301270189221935] <- {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(p) = \CarlsonsymellintRF@{p-x_{1}}{p-x_{2}}{p-x_{3}}} | (x + y*I)*(p) = 0.5*int(1/(sqrt(t+p - x[1])*sqrt(t+p - x[2])*sqrt(t+p - x[3])), t = 0..infinity) |
(x + y*I)*(p) == EllipticF[ArcCos[Sqrt[p - Subscript[x, 1]/p - Subscript[x, 3]]],(p - Subscript[x, 3]-p - Subscript[x, 2])/(p - Subscript[x, 3]-p - Subscript[x, 1])]/Sqrt[p - Subscript[x, 3]-p - Subscript[x, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[-0.7208699572238464, -0.7193085577979393] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.3758216901446034, -2.446030868401005] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{1} > x_{2}} | x[1] > x[2] |
Subscript[x, 1] > Subscript[x, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(\infty) = 0} | z*(infinity) = 0 |
z*(Infinity) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(x_{2}) = z(x_{1})+z(x_{3})} | (x + y*I)*(x[2]) = (x + y*I)*(x[1])+(x + y*I)*(x[3]) |
(x + y*I)*(Subscript[x, 2]) == (x + y*I)*(Subscript[x, 1])+(x + y*I)*(Subscript[x, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(x_{3}) = \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0}} | (x + y*I)*(x[3]) = 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity) |
(x + y*I)*(Subscript[x, 3]) == EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Plus[Complex[1.024519052838329, -0.27451905283832906], Times[Complex[-0.25881904510252074, -0.9659258262890683], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.27451905283832917, 1.0245190528383288], Times[Complex[-0.7239434227163943, -0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0} = -i\CarlsonsymellintRF@{0}{x_{1}-x_{3}}{x_{2}-x_{3}}} | 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity) = - I*0.5*int(1/(sqrt(t+0)*sqrt(t+x[1]- x[3])*sqrt(t+x[2]- x[3])), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]] == - I*EllipticF[ArcCos[Sqrt[0/Subscript[x, 2]- Subscript[x, 3]]],(Subscript[x, 2]- Subscript[x, 3]-Subscript[x, 1]- Subscript[x, 3])/(Subscript[x, 2]- Subscript[x, 3]-0)]/Sqrt[Subscript[x, 2]- Subscript[x, 3]-0] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-0.4754994064110389, 1.6461555153586378], Times[Complex[0.7239434227163943, 0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S = 3V\CarlsonsymellintRG@{a^{-2}}{b^{-2}}{c^{-2}}} | Error |
S == 3*V*Sqrt[(c)^(- 2)-(a)^(- 2)]*(EllipticE[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+(Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{S}{2\pi} = c^{2}+\frac{ab}{\sin@@{\phi}}\left(\incellintEk@{\phi}{k}\sin^{2}@@{\phi}+\incellintFk@{\phi}{k}\cos^{2}@@{\phi}\right)} | (S)/(2*Pi) = (c)^(2)+(a*b)/(sin(phi))*(EllipticE(sin(phi), k)*(sin(phi))^(2)+ EllipticF(sin(phi), k)*(cos(phi))^(2)) |
Divide[S,2*Pi] == (c)^(2)+Divide[a*b,Sin[\[Phi]]]*(EllipticE[\[Phi], (k)^2]*(Sin[\[Phi]])^(2)+ EllipticF[\[Phi], (k)^2]*(Cos[\[Phi]])^(2)) |
Failure | Failure | Failed [300 / 300] 300/300]: [[-4.910443424-.9759333290e-1*I <- {S = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 1}-5.505002077-.4622644670e-1*I <- {S = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-4.54039506540302, -0.09283854764917886] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 1], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-4.634568996487559, -0.31545051747139075] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 2], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.33#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\phi} = \frac{c}{a}} | cos(phi) = (c)/(a) |
Cos[\[Phi]] == Divide[c,a] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.2694569811-.3969495503*I <- {a = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I}.227765517+.4690753764*I <- {a = -3/2, c = -3/2, phi = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.06378043051909243, -0.10599798465255418] <- {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.061176166972244816, 0.11050836582743673] <- {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = \frac{a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}} | (k)^(2) = ((a)^(2)*((b)^(2)- (c)^(2)))/((b)^(2)*((a)^(2)- (c)^(2))) |
(k)^(2) == Divide[(a)^(2)*((b)^(2)- (c)^(2)),(b)^(2)*((a)^(2)- (c)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.33.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x^{2}}{a^{2}+\lambda}+\frac{y^{2}}{b^{2}+\lambda}+\frac{z^{2}}{c^{2}+\lambda} = 1} | ((x)^(2))/((a)^(2)+ lambda)+((y)^(2))/((b)^(2)+ lambda)+((x + y*I)^(2))/((c)^(2)+ lambda) = 1 |
Divide[(x)^(2),(a)^(2)+ \[Lambda]]+Divide[(y)^(2),(b)^(2)+ \[Lambda]]+Divide[(x + y*I)^(2),(c)^(2)+ \[Lambda]] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.33.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(\lambda) = Q\CarlsonsymellintRF@{a^{2}+\lambda}{b^{2}+\lambda}{c^{2}+\lambda}} | V*(lambda) = Q*0.5*int(1/(sqrt(t+(a)^(2)+ lambda)*sqrt(t+(b)^(2)+ lambda)*sqrt(t+(c)^(2)+ lambda)), t = 0..infinity) |
V*(\[Lambda]) == Q*EllipticF[ArcCos[Sqrt[(a)^(2)+ \[Lambda]/(c)^(2)+ \[Lambda]]],((c)^(2)+ \[Lambda]-(b)^(2)+ \[Lambda])/((c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda])]/Sqrt[(c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[-0.01914487900157147, 0.6670953471925876] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.08207662518407155, 0.5134467292285442] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1/C = \CarlsonsymellintRF@{a^{2}}{b^{2}}{c^{2}}} | 1/ C = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(b)^(2))*sqrt(t+(c)^(2))), t = 0..infinity) |
1/ C == EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]/Sqrt[(c)^(2)-(a)^(2)] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{c} = 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}} | L[c] = 2*Pi*a*b*c*int((1)/(sqrt(((a)^(2)+ lambda)*((b)^(2)+ lambda)*((c)^(2)+ lambda)^(3))), lambda = 0..infinity) |
Subscript[L, c] == 2*Pi*a*b*c*Integrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])*((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.33.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}} = V\CarlsonsymellintRD@{a^{2}}{b^{2}}{c^{2}}} | Error |
2*Pi*a*b*c*Integrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])*((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None] == V*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))])/(((c)^(2)-(b)^(2))*((c)^(2)-(a)^(2))^(1/2)) |
Missing Macro Error | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 19.33.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{a}+L_{b}+L_{c} = 4\pi} | L[a]+ L[b]+ L[c] = 4*Pi |
Subscript[L, a]+ Subscript[L, b]+ Subscript[L, c] == 4*Pi |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}} | a*b*int(((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*cos(theta))^(- 1/ 2)* cos(theta), theta = 0..2*Pi) = 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) |
a*b*Integrate[((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*Cos[\[Theta]])^(- 1/ 2)* Cos[\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})} | 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) = 2*a*b*I*(e[5]) |
2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None] == 2*a*b*I*(Subscript[e, 5]) |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-3.959693187-6.593729744*I <- {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = 1/2*3^(1/2)+1/2*I}2.187421133-4.946615428*I <- {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 19.34#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = h^{2}+a^{2}+b^{2}} | a[3] = (h)^(2)+ (a)^(2)+ (b)^(2) |
Subscript[a, 3] == (h)^(2)+ (a)^(2)+ (b)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{5} = 0} | a[5] = 0 |
Subscript[a, 5] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{5} = 1} | b[5] = 1 |
Subscript[b, 5] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})} | 2*a*b*I*(e[5]) = a[3]*I*(0)- I*(e[3]) |
2*a*b*I*(Subscript[e, 5]) == Subscript[a, 3]*I*(0)- I*(Subscript[e, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{+}^{2} = a_{3}+ 2ab} | (r[+])^(2) = a[3]+ 2*a*b |
(Subscript[r, +])^(2) == Subscript[a, 3]+ 2*a*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = \CarlsonsymellintRF@{z_{1}}{z_{2}}{z_{3}}} | 0.5*int(1/(sqrt(t+1)*sqrt(t+2)*sqrt(t+4)), t = 0..infinity) = 0.5*int(1/(sqrt(t+z[1])*sqrt(t+z[2])*sqrt(t+z[3])), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == EllipticF[ArcCos[Sqrt[Subscript[z, 1]/Subscript[z, 3]]],(Subscript[z, 3]-Subscript[z, 2])/(Subscript[z, 3]-Subscript[z, 1])]/Sqrt[Subscript[z, 3]-Subscript[z, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6113291272616378, 0.7460602493090597] <- {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{aligned} \displaystyle z_{1}&\displaystyle = 2.10985\;99098\;8,\\ \displaystyle z_{3}&\displaystyle} | |
|
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = 0.68508\;58166\dots} | 0.5*int(1/(sqrt(t+1)*sqrt(t+2)*sqrt(t+4)), t = 0..infinity) = 0.6850858166 |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 0.6850858166 |
Failure | Failure | Successful [Tested: 0] | Successful [Tested: 1] |
| 19.36#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2a_{n+1} = a_{n}+\sqrt{a_{n}^{2}-c_{n}^{2}}} | 2*a[n + 1] = sqrt(a(a[n])^(2)- c(c[n])^(2)) |
2*Subscript[a, n + 1] == Sqrt[a(Subscript[a, n])^(2)- c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2c_{n+1} = a_{n}-\sqrt{a_{n}^{2}-c_{n}^{2}}} | 2*c[n + 1] = sqrt(a(a[n])^(2)- c(c[n])^(2)) |
2*Subscript[c, n + 1] == Sqrt[a(Subscript[a, n])^(2)- c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2t_{n+1} = t_{n}+\sqrt{t_{n}^{2}+\theta c_{n}^{2}}} | 2*t[n + 1] = sqrt(t(t[n])^(2)+ theta*c(c[n])^(2)) |
2*Subscript[t, n + 1] == Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < c_{0}} | 0 < c[0] |
0 < Subscript[c, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0} \geq 0} | t[0] >= 0 |
Subscript[t, 0] >= 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0}^{2}+\theta a_{0}^{2} \geq 0} | (t[0])^(2)+ theta*(a[0])^(2) >= 0 |
(Subscript[t, 0])^(2)+ \[Theta]*(Subscript[a, 0])^(2) >= 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta = + 1} | theta = + 1 |
\[Theta] == + 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}}} | 0.5*int(1/(sqrt(t+t(t[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*c(c[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*a(a[0])^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(T)^(2))*sqrt(t+(T)^(2))*sqrt(t+(T)^(2)+ theta*(M)^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[t(Subscript[t, 0])^(2)/t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)]],(t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2)+ \[Theta]*c(Subscript[c, 0])^(2))/(t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2))]/Sqrt[t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2)] == EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta]*(M)^(2)]],((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))/((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta]*(M)^(2)-(T)^(2)] |
Error | Failure | - | Failed [300 / 300] {Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284271247461903, Power[Times[Complex[0.0, 1.0], a], Rational[-1, 2]], EllipticF[ArcCos[Power[Plus[Complex[-0.031249999999999986, 0.05412658773652742], Times[Complex[0.0, 0.125], a]], Rational[1, 2]]], Times[Complex[0.0, -8.0], Power[a, -1], Plus[Times[Complex[0.0, 0.125], a], Times[Complex[0.0, 0.125], c]]]]]] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[c, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[t, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284
|
| 19.36.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}} = \CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}} | Error |
EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta]*(M)^(2)]],((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))/((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta]*(M)^(2)-(T)^(2)] == 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta]*(M)^(2))/((T)^(2))] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-1.634056915706757, -0.008820605997006181] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.6914869520542948, 0.13073697514602478] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3}^{2} = 2.46209\;30206\;0} | (a[3])^(2) = 2.46209302060 |
(Subscript[a, 3])^(2) == 2.46209302060 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{3}^{2} = 1.46971\;53173\;1} | (t[3])^(2) = 1.46971531731 |
(Subscript[t, 3])^(2) == 1.46971531731 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = \CarlsonellintRC@{T^{2}+M^{2}}{T^{2}}} | Error |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))] |
Missing Macro Error | Failure | - | Failed [100 / 100]
{Complex[-0.841498016533642, 0.8813735870195429] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.8857105197615976, -2.720699010523131] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{T^{2}+M^{2}}{T^{2}} = 0.68508\;58166} | Error |
1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))] == 0.6850858166 |
Missing Macro Error | Failure | - | Failed [100 / 100]
{Complex[0.8414980165670778, -0.8813735870195429] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.8857105197950335, 2.720699010523131] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{n} = \sqrt{t_{n}^{2}+\theta a_{n}^{2}}} | sqrt(t(t[n])^(2)+ theta*a(a[n])^(2)) |
Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*a(Subscript[a, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{n} = h_{n-1}\frac{t_{n}}{\sqrt{t_{n}^{2}+\theta c_{n}^{2}}}} | h[n] (t[n])/(sqrt(t(t[n])^(2)+ theta*c(c[n])^(2))) |
Subscript[h, n] Divide[Subscript[t, n],Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*c(Subscript[c, n])^(2)]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \left(t_{0}^{2}+\theta\sum_{m=0}^{\infty}2^{m-1}c_{m}^{2}\right)\CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}+h_{0}+\sum_{m=1}^{\infty}2^{m}(h_{m}-h_{m-1})} | Error |
(t(Subscript[t, 0])^(2)+ \[Theta]*Sum[(2)^(m - 1)* c(Subscript[c, m])^(2), {m, 0, Infinity}, GenerateConditions->None])* 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta]*(M)^(2))/((T)^(2))]+ Subscript[h, 0]+ Sum[(2)^(m)*(Subscript[h, m]- Subscript[h, m - 1]), {m, 1, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Failed [1 / 1]
|