19.22

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.22.E1	${\displaystyle{\displaystyle R_{F}\left(0,x^{2},y^{2}\right)=R_{F}\left(0,xy,a^{2}\right)}}$ \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] Result: Complex[0.1731783664325578, 0.8740191847640398] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Complex[0.4406854652170371, 0.9732684211375591] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]} ... skip entries to safe data
19.22.E2	${\displaystyle{\displaystyle 2R_{G}\left(0,x^{2},y^{2}\right)=4R_{G}\left(0,xy,a^{2}\right)-xyR_{F}\left(0,xy,a^{2}\right)}}$ 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] Result: Complex[-0.848574889541176, -1.6278775384876862] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: -2.356194490192345 Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22.E3	${\displaystyle{\displaystyle 2y^{2}R_{D}\left(0,x^{2},y^{2}\right)=\tfrac{1}{4}(y^{2}-x^{2})R_{D}\left(0,xy,a^{2}\right)+3R_{F}\left(0,xy,a^{2}\right)}}$ 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] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22.E4	${\displaystyle{\displaystyle(p_{+}^{2}-p_{-}^{2})R_{J}\left(0,x^{2},y^{2},p^{2}\right)=2(p_{+}^{2}-a^{2})R_{J}\left(0,xy,a^{2},p_{+}^{2}\right)-3R_{F}\left(0,xy,a^{2}\right)+3\pi/(2p)}}$ (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	((Subscript[p, +])^(2)- (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] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-(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	${\displaystyle{\displaystyle(p_{-}^{2}-p_{+}^{2})R_{J}\left(0,x^{2},y^{2},p^{2}\right)=2(p_{-}^{2}-a^{2})R_{J}\left(0,xy,a^{2},p_{-}^{2}\right)-3R_{F}\left(0,xy,a^{2}\right)+3\pi/(2p)}}$ (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	((Subscript[p, -])^(2)- (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] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((a)^(2)-0)/((a)^(2)-(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-(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	${\displaystyle{\displaystyle p_{+}p_{-}=pa}}$ p_{+}p_{-} = pa		p[+]*p[-] = p*a	Subscript[p, +]*Subscript[p, -] == p*a	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex2	${\displaystyle{\displaystyle p_{+}^{2}+p_{-}^{2}=p^{2}+xy}}$ 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	${\displaystyle{\displaystyle p_{+}^{2}-p_{-}^{2}=\sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}}}$ p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}		(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	${\displaystyle{\displaystyle 4(p_{+}^{2}-a^{2})=(\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}}}$ 4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}		4*((p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2)	4*((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	${\displaystyle{\displaystyle 2p^{2}R_{J}\left(0,x^{2},y^{2},p^{2}\right)=v_{+}v_{-}R_{J}\left(0,xy,a^{2},v^{2}_{+}\right)+3R_{F}\left(0,xy,a^{2}\right)}}$ 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}}	${\displaystyle{\displaystyle v_{+}=(p^{2}+xy)/(2p),v_{-}=(p^{2}-xy)/(2p)}}$	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, +]*Subscript[v, -]*3*((a)^(2)-0)/((a)^(2)-(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-(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	${\displaystyle{\displaystyle\frac{2}{\pi}R_{F}\left(0,a_{0}^{2},g_{0}^{2}\right)=\frac{1}{M\left(a_{0},g_{0}\right)}}}$ \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}		(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0]))	Error	Aborted	Missing Macro Error	Skipped - Because timed out	-
19.22.E9	${\displaystyle{\displaystyle\frac{1}{M\left(a_{0},g_{0}\right)}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)=\frac{1}{M\left(a_{0},g_{0}\right)}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)}}$ \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)		(1)/(GaussAGM(a[0], g[0]))*((a[0])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 0..infinity)) = (1)/(GaussAGM(a[0], g[0]))*((a[1])^(2)- sum((2)^(n - 1)* (c[n])^(2), n = 2..infinity))	Error	Failure	Missing Macro Error	Error	-
19.22#Ex5	${\displaystyle{\displaystyle Q_{0}=1}}$ Q_{0} = 1		Q[0] = 1	Subscript[Q, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex6	${\displaystyle{\displaystyle Q_{n+1}=\tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}}}$ 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	${\displaystyle{\displaystyle p_{n+1}=\frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}}}$ p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}		p[n + 1] = ((p[n])^(2)+ a[n]*g[n])/(2*p[n])	Subscript[p, n + 1] == Divide[(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	${\displaystyle{\displaystyle\varepsilon_{n}=\frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}}}$ \varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}		varepsilon[n] = ((p[n])^(2)- a[n]*g[n])/((p[n])^(2)+ a[n]*g[n])	Subscript[\[CurlyEpsilon], n] == Divide[(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex9	${\displaystyle{\displaystyle Q_{0}=1}}$ Q_{0} = 1		Q[0] = 1	Subscript[Q, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex10	${\displaystyle{\displaystyle Q_{n+1}=\tfrac{1}{2}Q_{n}\varepsilon_{n}}}$ 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	${\displaystyle{\displaystyle p_{0}^{2}=a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})}}$ p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})		(p[0])^(2) = (a[0])^(2)*((q[0])^(2)+ (g[0])^(2))/((q[0])^(2)+ (a[0])^(2))	(Subscript[p, 0])^(2) == (Subscript[a, 0])^(2)*((Subscript[q, 0])^(2)+ (Subscript[g, 0])^(2))/((Subscript[q, 0])^(2)+ (Subscript[a, 0])^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex11	${\displaystyle{\displaystyle a=(x+y)/2}}$ a = (x+y)/2		a = (x + y)/2	a == (x + y)/2	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex12	${\displaystyle{\displaystyle 2z_{+}=\sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}}}$ 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	${\displaystyle{\displaystyle z_{+}z_{-}=za}}$ z_{+}z_{-} = za		z[+]*z[-] = z*a	Subscript[z, +]*Subscript[z, -] == z*a	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex14	${\displaystyle{\displaystyle z_{+}^{2}+z_{-}^{2}=z^{2}+xy}}$ 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	${\displaystyle{\displaystyle z_{+}^{2}-z_{-}^{2}=\sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}}}$ 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	${\displaystyle{\displaystyle 4(z_{+}^{2}-a^{2})=(\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}}}$ 4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}		4*((x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2)	4*((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	${\displaystyle{\displaystyle R_{F}\left(x^{2},y^{2},z^{2}\right)=R_{F}\left(a^{2},z_{-}^{2},z_{+}^{2}\right)}}$ \CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}		0.5*int(1/(sqrt(t+(x)^(2))*sqrt(t+(y)^(2))*sqrt(t+(x + y*I)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I[-])^(2))*sqrt(t+(x + y*I[+])^(2))), t = 0..infinity)	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)] == EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(Subscript[x + y*I, +])^(2)-(a)^(2)]	Error	Failure	-	Error
19.22.E19	${\displaystyle{\displaystyle(z_{+}^{2}-z_{-}^{2})R_{D}\left(x^{2},y^{2},z^{2}\right)={2(z_{+}^{2}-a^{2})}R_{D}\left(a^{2},z_{-}^{2},z_{+}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+(3/z)}}$ (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	((Subscript[x + y*I, +])^(2)-(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)) == 2*((Subscript[x + y*I, +])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, +])^(2)]],((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))/((Subscript[x + y*I, +])^(2)-(a)^(2))])/(((Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2))*((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	${\displaystyle{\displaystyle(z_{-}^{2}-z_{+}^{2})R_{D}\left(x^{2},y^{2},z^{2}\right)={2(z_{-}^{2}-a^{2})}R_{D}\left(a^{2},z_{+}^{2},z_{-}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+(3/z)}}$ (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	((Subscript[x + y*I, -])^(2)-(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)) == 2*((Subscript[x + y*I, -])^(2)- (a)^(2))*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/(((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))*((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	${\displaystyle{\displaystyle(p_{+}^{2}-p_{-}^{2})R_{J}\left(x^{2},y^{2},z^{2},p^{2}\right)=2(p_{+}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{+}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}\right)}}$ (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	((Subscript[p, +])^(2)- (Subscript[p, -])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-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)] == 2*((Subscript[p, +])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(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	${\displaystyle{\displaystyle(p_{-}^{2}-p_{+}^{2})R_{J}\left(x^{2},y^{2},z^{2},p^{2}\right)=2(p_{-}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{-}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}\right)}}$ (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	((Subscript[p, -])^(2)- (Subscript[p, +])^(2))*3*((x + y*I)^(2)-(x)^(2))/((x + y*I)^(2)-(p)^(2))*(EllipticPi[((x + y*I)^(2)-(p)^(2))/((x + y*I)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-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)] == 2*((Subscript[p, -])^(2)- (a)^(2))*3*((Subscript[x + y*I, -])^(2)-(a)^(2))/((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))*(EllipticPi[((Subscript[x + y*I, -])^(2)-(Subscript[p, -])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(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	${\displaystyle{\displaystyle 2R_{G}\left(x^{2},y^{2},z^{2}\right)=4R_{G}\left(a^{2},z_{+}^{2},z_{-}^{2}\right)-xyR_{F}\left(x^{2},y^{2},z^{2}\right)-z}}$ 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]) == 4*Sqrt[(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]],((Subscript[x + y*I, -])^(2)-(Subscript[x + y*I, +])^(2))/((Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(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	${\displaystyle{\displaystyle R_{C}\left(x^{2},y^{2}\right)=R_{C}\left(a^{2},ay\right)}}$ \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] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22#Ex17	${\displaystyle{\displaystyle x+y=2a}}$ x+y = 2a		x + y = 2*a	x + y == 2*a	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex18	${\displaystyle{\displaystyle x-y=(\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}}}$ x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}		x - y = ((2)/(a))*sqrt(((a)^(2)-(x + y*I[+])^(2))*((a)^(2)-(x + y*I[-])^(2)))	x - y == (Divide[2,a])*Sqrt[((a)^(2)-(Subscript[x + y*I, +])^(2))*((a)^(2)-(Subscript[x + y*I, -])^(2))]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex19	${\displaystyle{\displaystyle z=\ifrac{z_{+}z_{-}}{a}}}$ z = \ifrac{z_{+}z_{-}}{a}		z = (z[+]*z[-])/(a)	z == Divide[Subscript[z, +]*Subscript[z, -],a]	Skipped - no semantic math	Skipped - no semantic math	-	-