19.24: Difference between revisions

Latest revision as of 11:52, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.24.E1	${\displaystyle{\displaystyle\ln 4\leq\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{% y/z}}}$ `\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}`	${\displaystyle{\displaystyle 0<y,y\leq z}}$	ln(4) <= sqrt(x + yI)0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)+ ln(sqrt(y/(x + y*I)))	Log[4] <= Sqrt[x + yI]EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0]+ Log[Sqrt[y/(x + y*I)]]	Error	Failure	-	Failed [9 / 9] Result: LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[1.3862943611198906, Complex[0.6277320470267476, -0.9602476282953896]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E1	${\displaystyle{\displaystyle\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{y/z}\leq% \tfrac{1}{2}\pi}}$ `\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi`	${\displaystyle{\displaystyle 0<y,y\leq z}}$	sqrt(x + yI)0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)+ ln(sqrt(y/(x + yI))) <= (1)/(2)Pi	Sqrt[x + yI]EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0]+ Log[Sqrt[y/(x + yI)]] <= Divide[1,2]Pi	Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[0.6277320470267476, -0.9602476282953896], 1.5707963267948966] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E2	${\displaystyle{\displaystyle\tfrac{1}{2}\leq z^{-1/2}R_{G}\left(0,y,z\right)}}$ `\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}`	${\displaystyle{\displaystyle 0\leq y,y\leq z}}$	Error	Divide[1,2] <= (x + yI)^(- 1/2) Sqrt[x + yI-0](EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+(Cot[ArcCos[Sqrt[0/x + yI]]])^2EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+Cot[ArcCos[Sqrt[0/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/x + yI]]]^2])	Missing Macro Error	Failure	-	Failed [9 / 9] Result: 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]]]]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: 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]]]]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E2	${\displaystyle{\displaystyle z^{-1/2}R_{G}\left(0,y,z\right)\leq\tfrac{1}{4}% \pi}}$ `z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi`	${\displaystyle{\displaystyle 0\leq y,y\leq z}}$	Error	(x + yI)^(- 1/2) Sqrt[x + yI-0](EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+(Cot[ArcCos[Sqrt[0/x + yI]]])^2EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+Cot[ArcCos[Sqrt[0/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/x + yI]]]^2]) <= Divide[1,4]*Pi	Missing Macro Error	Failure	-	Failed [9 / 9] Result: 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] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: 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] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E3	${\displaystyle{\displaystyle\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3}\leq% \frac{4}{\pi}R_{G}\left(0,y^{2},z^{2}\right)}}$ `\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}`	${\displaystyle{\displaystyle y>0,z>0}}$	Error	(Divide[(y)^(3/2)+(x + yI)^(3/2),2])^(2/3) <= Divide[4,Pi]Sqrt[(x + yI)^(2)-0](EllipticE[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(x + yI)^(2)]]]^2])	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[1.0588191704631045, 0.29794136993360365], Complex[2.118851869395612, 0.5983245902184247]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E3	${\displaystyle{\displaystyle\frac{4}{\pi}R_{G}\left(0,y^{2},z^{2}\right)\leq% \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}}}$ `\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}`	${\displaystyle{\displaystyle y>0,z>0}}$	Error	Divide[4,Pi]Sqrt[(x + yI)^(2)-0](EllipticE[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(x + yI)^(2)]]]^2]) <= (Divide[(y)^(2)+(x + yI)^(2),2])^(1/2)	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[2.118851869395612, 0.5983245902184247], Complex[1.112897508375995, 0.3369582528288897]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E4	${\displaystyle{\displaystyle\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2}\leq\frac{4}{3% \pi}R_{J}\left(0,y,z,p\right)}}$ `\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}`		Error	Divide[2,Sqrt[p]](2y(x + yI)+ yp +(x + yI)p)^(- 1/2) <= Divide[4,3Pi]3(x + yI-0)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-0),ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]-EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)])/Sqrt[x + yI-0]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7797231369520263, -0.6247258696161743], Complex[-0.6706782382611747, 0.54526856836685]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E4	${\displaystyle{\displaystyle\frac{4}{3\pi}R_{J}\left(0,y,z,p\right)\leq(yzp^{2% })^{-3/8}}}$ `\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}`		Error	Divide[4,3Pi]3(x + yI-0)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-0),ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]-EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)])/Sqrt[x + yI-0] <= (y(x + yI)(p)^(2))^(- 3/8)	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.6706782382611747, 0.54526856836685], Complex[0.8422602311268256, -0.6912251080442312]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E5	${\displaystyle{\displaystyle\frac{1}{a_{n}}\leq\frac{2}{\pi}R_{F}\left(0,a_{0}% ^{2},g_{0}^{2}\right)}}$ `\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}`		(1)/(a[n]) <= (2)/(Pi)0.5int(1/(sqrt(t+0)sqrt(t+(a[0])^(2))sqrt(t+(g[0])^(2))), t = 0..infinity)	Divide[1,Subscript[a, n]] <= Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: 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]]]]] Test Values: {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]]]]} Result: 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[-0.12499999999999994, -0.21650635094610968], g]], Power[g, -1]]]]] Test Values: {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[2, 3]], Pi]]]]} ... skip entries to safe data
19.24.E5	${\displaystyle{\displaystyle\frac{2}{\pi}R_{F}\left(0,a_{0}^{2},g_{0}^{2}% \right)\leq\frac{1}{g_{n}}}}$ `\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}`		(2)/(Pi)0.5int(1/(sqrt(t+0)sqrt(t+(a[0])^(2))sqrt(t+(g[0])^(2))), t = 0..infinity) <= (1)/(g[n])	Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: 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]] Test Values: {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]]]]} Result: 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[-0.9999999999999996, -1.7320508075688774]] Test Values: {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[2, 3]], Pi]]]]} ... skip entries to safe data
19.24#Ex1	${\displaystyle{\displaystyle a_{n+1}=(a_{n}+g_{n})/2}}$ `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	${\displaystyle{\displaystyle g_{n+1}=\sqrt{a_{n}g_{n}}}}$ `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	${\displaystyle{\displaystyle L(a,b)=8R_{G}\left(0,a^{2},b^{2}\right)}}$ `L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}`		Error	L[a , b] == 8Sqrt[(b)^(2)-0](EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2EllipticF[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	${\displaystyle{\displaystyle R_{F}\left(x,y,0\right)R_{G}\left(x,y,0\right)>% \tfrac{1}{8}\pi^{2}}}$ `\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]]])^2EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/0]]]^2]) > Divide[1,8](Pi)^(2)	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Greater[Indeterminate, 1.2337005501361697] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Indeterminate, 1.2337005501361697] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex4	${\displaystyle{\displaystyle R_{F}\left(x,y,0\right)+2R_{G}\left(x,y,0\right)>% \pi}}$ `\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi`		Error	EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]+ 2Sqrt[0-x](EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2EllipticF[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] Result: Greater[Indeterminate, 3.141592653589793] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Indeterminate, 3.141592653589793] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E9	${\displaystyle{\displaystyle\frac{1}{2}\,g_{1}^{2}\leq\frac{R_{G}\left(a_{0}^{% 2},g_{0}^{2},0\right)}{R_{F}\left(a_{0}^{2},g_{0}^{2},0\right)}}}$ `\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[1,2](Subscript[g, 1])^(2) <= Divide[Sqrt[0-(Subscript[a, 0])^(2)](EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate] Test Values: {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]]]]} Result: LessEqual[Complex[-0.06249999999999997, -0.10825317547305484], Indeterminate] Test Values: {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]]]]} ... skip entries to safe data
19.24.E9	${\displaystyle{\displaystyle\frac{R_{G}\left(a_{0}^{2},g_{0}^{2},0\right)}{R_{% F}\left(a_{0}^{2},g_{0}^{2},0\right)}\leq\frac{1}{2}\,a_{1}^{2}}}$ `\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-(Subscript[a, 0])^(2)](EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2)	Missing Macro Error	Failure	-	Failed [300 / 300] Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] Test Values: {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]]]]} Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] Test Values: {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]]]]} ... skip entries to safe data
19.24.E10	${\displaystyle{\displaystyle\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}}\leq R_{F}% \left(x,y,z\right)}}$ `\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}`		(3)/(sqrt(x)+sqrt(y)+sqrt(x + yI)) <= 0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + y*I)), t = 0..infinity)	Divide[3,Sqrt[x]+Sqrt[y]+Sqrt[x + yI]] <= EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + y*I-x]	Aborted	Failure	Error	Failed [18 / 18] Result: LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7738030002696183, -0.11364498174072818], Complex[-0.28823404661462, -0.7809212115368181]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E10	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)\leq\frac{1}{(xyz)^{1/6}}}}$ `\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}`		0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) <= (1)/((xy(x + y*I))^(1/6))	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] <= Divide[1,(xy(x + y*I))^(1/6)]	Aborted	Failure	Error	Failed [18 / 18] Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.7640769591692358, -0.10059264002361257]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E11	${\displaystyle{\displaystyle\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p% }}\right)^{3}\leq R_{J}\left(x,y,z,p\right)}}$ `\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 + yI]+ 2Sqrt[p]])^(3) <= 3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + y*I-x]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7477899794343462, -0.4392695700678081], Complex[-0.36602768453446033, 0.5058947820270108]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E11	${\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)\leq(xyzp^{2})^{-3/10}}}$ `\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}`		Error	3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x] <= (xy(x + yI)*(p)^(2))^(- 3/10)	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.36602768453446033, 0.5058947820270108], Complex[0.8086249764673956, -0.49552602288885395]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E12	${\displaystyle{\displaystyle\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z})\leq R_{G}% \left(x,y,z\right)}}$ `\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}`		Error	Divide[1,3](Sqrt[x]+Sqrt[y]+Sqrt[x + yI]) <= Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2])	Missing Macro Error	Failure	-	Failed [18 / 18] Result: 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]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: 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]]]]]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex7	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)R_{G}\left(x,y,z\right)>1}}$ `\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1`		Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 1	Missing Macro Error	Failure	-	Failed [18 / 18] Result: 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] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: 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] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex8	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)+R_{G}\left(x,y,z\right)>2}}$ `\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2`		Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]+ Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2]) > 2	Missing Macro Error	Failure	-	Failed [18 / 18] Result: 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] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: 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] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E15	${\displaystyle{\displaystyle R_{C}\left(x,\tfrac{1}{2}(y+z)\right)\leq R_{F}% \left(x,y,z\right)}}$ `\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}`	${\displaystyle{\displaystyle x\geq 0}}$	Error	1/Sqrt[Divide[1,2](y +(x + yI))]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Divide[1,2](y +(x + yI)))] <= EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + y*I-x]	Missing Macro Error	Failure	-	Failed [18 / 18] Result: LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7805167095081702, -0.12346643314922054], Complex[-0.28823404661462, -0.7809212115368181]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E15	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)\leq R_{C}\left(x,\sqrt{yz% }\right)}}$ `\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}`	${\displaystyle{\displaystyle x\geq 0}}$	Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] <= 1/Sqrt[Sqrt[y(x + yI)]]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Sqrt[y(x + y*I)])]	Missing Macro Error	Failure	-	Failed [18 / 18] Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.765857524311696, -0.1031964554328576]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/19.24.E1 19.24.E1] || [[Item:Q6482|<math>\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}</syntaxhighlight> || <math>0 < y, y \leq z</math> || <syntaxhighlight lang=mathematica>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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]]
+| [https://dlmf.nist.gov/19.24.E1 19.24.E1] || <math qid="Q6482">\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}</syntaxhighlight> || <math>0 < y, y \leq z</math> || <syntaxhighlight lang=mathematica>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)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[1.3862943611198906, Complex[0.6277320470267476, -0.9602476282953896]]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E1 19.24.E1] || [[Item:Q6482|<math>\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi</syntaxhighlight> || <math>0 < y, y \leq z</math> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966]
+| [https://dlmf.nist.gov/19.24.E1 19.24.E1] || <math qid="Q6482">\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi</syntaxhighlight> || <math>0 < y, y \leq z</math> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.6277320470267476, -0.9602476282953896], 1.5707963267948966]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E2 19.24.E2] || [[Item:Q6483|<math>\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}</syntaxhighlight> || <math>0 \leq y, y \leq z</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]
+| [https://dlmf.nist.gov/19.24.E2 19.24.E2] || <math qid="Q6483">\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}</syntaxhighlight> || <math>0 \leq y, y \leq z</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]]]]]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E2 19.24.E2] || [[Item:Q6483|<math>z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi</syntaxhighlight> || <math>0 \leq y, y \leq z</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
+| [https://dlmf.nist.gov/19.24.E2 19.24.E2] || <math qid="Q6483">z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi</syntaxhighlight> || <math>0 \leq y, y \leq z</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E3 19.24.E3] || [[Item:Q6484|<math>\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}</syntaxhighlight> || <math>y > 0, z > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]]
+| [https://dlmf.nist.gov/19.24.E3 19.24.E3] || <math qid="Q6484">\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}</syntaxhighlight> || <math>y > 0, z > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.0588191704631045, 0.29794136993360365], Complex[2.118851869395612, 0.5983245902184247]]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E3 19.24.E3] || [[Item:Q6484|<math>\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}</syntaxhighlight> || <math>y > 0, z > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]]
+| [https://dlmf.nist.gov/19.24.E3 19.24.E3] || <math qid="Q6484">\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}</syntaxhighlight> || <math>y > 0, z > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[2.118851869395612, 0.5983245902184247], Complex[1.112897508375995, 0.3369582528288897]]
 Test Values: {Rule[x, 1.5], Rule[y, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E4 19.24.E4] || [[Item:Q6485|<math>\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]]
+| [https://dlmf.nist.gov/19.24.E4 19.24.E4] || <math qid="Q6485">\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7797231369520263, -0.6247258696161743], Complex[-0.6706782382611747, 0.54526856836685]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E4 19.24.E4] || [[Item:Q6485|<math>\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]]
+| [https://dlmf.nist.gov/19.24.E4 19.24.E4] || <math qid="Q6485">\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.6706782382611747, 0.54526856836685], Complex[0.8422602311268256, -0.6912251080442312]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E5 19.24.E5] || [[Item:Q6486|<math>\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(a[n]) <= (2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Subscript[a, n]] <= Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]
+| [https://dlmf.nist.gov/19.24.E5 19.24.E5] || <math qid="Q6486">\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(a[n]) <= (2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Subscript[a, n]] <= Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]
 Test Values: {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]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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[-0.12499999999999994, -0.21650635094610968], g]], Power[g, -1]]]]]
 Test Values: {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[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E5 19.24.E5] || [[Item:Q6486|<math>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) <= (1)/(g[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]
+| [https://dlmf.nist.gov/19.24.E5 19.24.E5] || <math qid="Q6486">\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a[0])^(2))*sqrt(t+(g[0])^(2))), t = 0..infinity) <= (1)/(g[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]
 Test Values: {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]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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[-0.9999999999999996, -1.7320508075688774]]
 Test Values: {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[2, 3]], Pi]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/19.24#Ex1 19.24#Ex1] || [[Item:Q6487|<math>a_{n+1} = (a_{n}+g_{n})/2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n+1} = (a_{n}+g_{n})/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n + 1] = (a[n]+ g[n])/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n + 1] == (Subscript[a, n]+ Subscript[g, n])/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/19.24#Ex1 19.24#Ex1] || <math qid="Q6487">a_{n+1} = (a_{n}+g_{n})/2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n+1} = (a_{n}+g_{n})/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n + 1] = (a[n]+ g[n])/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n + 1] == (Subscript[a, n]+ Subscript[g, n])/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/19.24#Ex2 19.24#Ex2] || [[Item:Q6488|<math>g_{n+1} = \sqrt{a_{n}g_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>g_{n+1} = \sqrt{a_{n}g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">g[n + 1] = sqrt(a[n]*g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/19.24#Ex2 19.24#Ex2] || <math qid="Q6488">g_{n+1} = \sqrt{a_{n}g_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>g_{n+1} = \sqrt{a_{n}g_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">g[n + 1] = sqrt(a[n]*g[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/19.24.E7 19.24.E7] || [[Item:Q6489|<math>L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || Error
+| [https://dlmf.nist.gov/19.24.E7 19.24.E7] || <math qid="Q6489">L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/19.24#Ex3 19.24#Ex3] || [[Item:Q6490|<math>\CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 1.2337005501361697]
+| [https://dlmf.nist.gov/19.24#Ex3 19.24#Ex3] || <math qid="Q6490">\CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 1.2337005501361697]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 1.2337005501361697]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24#Ex4 19.24#Ex4] || [[Item:Q6491|<math>\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 3.141592653589793]
+| [https://dlmf.nist.gov/19.24#Ex4 19.24#Ex4] || <math qid="Q6491">\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 3.141592653589793]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Greater[Indeterminate, 3.141592653589793]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E9 19.24.E9] || [[Item:Q6492|<math>\frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(Subscript[g, 1])^(2) <= Divide[Sqrt[0-(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate]
+| [https://dlmf.nist.gov/19.24.E9 19.24.E9] || <math qid="Q6492">\frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*(Subscript[g, 1])^(2) <= Divide[Sqrt[0-(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate]
 Test Values: {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]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.06249999999999997, -0.10825317547305484], Indeterminate]
 Test Values: {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]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E9 19.24.E9] || [[Item:Q6492|<math>\frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Sqrt[0-(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]]
+| [https://dlmf.nist.gov/19.24.E9 19.24.E9] || <math qid="Q6492">\frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Sqrt[0-(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]]
 Test Values: {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]]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]]
 Test Values: {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]]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E10 19.24.E10] || [[Item:Q6493|<math>\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Aborted || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]]
+| [https://dlmf.nist.gov/19.24.E10 19.24.E10] || <math qid="Q6493">\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Aborted || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7738030002696183, -0.11364498174072818], Complex[-0.28823404661462, -0.7809212115368181]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E10 19.24.E10] || [[Item:Q6493|<math>\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]</syntaxhighlight> || Aborted || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]]
+| [https://dlmf.nist.gov/19.24.E10 19.24.E10] || <math qid="Q6493">\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]</syntaxhighlight> || Aborted || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.7640769591692358, -0.10059264002361257]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E11 19.24.E11] || [[Item:Q6494|<math>\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]]
+| [https://dlmf.nist.gov/19.24.E11 19.24.E11] || <math qid="Q6494">\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7477899794343462, -0.4392695700678081], Complex[-0.36602768453446033, 0.5058947820270108]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E11 19.24.E11] || [[Item:Q6494|<math>\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]]
+| [https://dlmf.nist.gov/19.24.E11 19.24.E11] || <math qid="Q6494">\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.36602768453446033, 0.5058947820270108], Complex[0.8086249764673956, -0.49552602288885395]]
 Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E12 19.24.E12] || [[Item:Q6495|<math>\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]]
+| [https://dlmf.nist.gov/19.24.E12 19.24.E12] || <math qid="Q6495">\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]]]]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]]]]]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24#Ex7 19.24#Ex7] || [[Item:Q6498|<math>\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
+| [https://dlmf.nist.gov/19.24#Ex7 19.24#Ex7] || <math qid="Q6498">\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24#Ex8 19.24#Ex8] || [[Item:Q6499|<math>\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
+| [https://dlmf.nist.gov/19.24#Ex8 19.24#Ex8] || <math qid="Q6499">\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E15 19.24.E15] || [[Item:Q6500|<math>\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]]
+| [https://dlmf.nist.gov/19.24.E15 19.24.E15] || <math qid="Q6500">\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7805167095081702, -0.12346643314922054], Complex[-0.28823404661462, -0.7809212115368181]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/19.24.E15 19.24.E15] || [[Item:Q6500|<math>\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)])]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]]
+| [https://dlmf.nist.gov/19.24.E15 19.24.E15] || <math qid="Q6500">\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)])]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]]
 Test Values: {Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.765857524311696, -0.1031964554328576]]
 Test Values: {Rule[x, 1.5], Rule[y, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |}
 </div>

19.24: Difference between revisions

Latest revision as of 11:52, 28 June 2021

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