19.30

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.30#Ex1	${\displaystyle{\displaystyle x=a\sin\phi}}$ x = a\sin@@{\phi}		x = a*sin(phi)	x == a*Sin[\[Phi]]	Failure	Failure	Failed [180 / 180] Result: 2.788470502+.5063946946*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 3/2} Result: 1.788470502+.5063946946*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[2.1491827752870476, 0.34394646701016035] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.093555858156998, 0.6491787480429551] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30#Ex2	${\displaystyle{\displaystyle y=b\cos\phi}}$ y = b\cos@@{\phi}	${\displaystyle{\displaystyle 0\leq\phi,\phi\leq 2\pi}}$	y = b*cos(phi)	y == b*Cos[\[Phi]]	Failure	Failure	Failed [108 / 108] Result: -1.393894198 Test Values: {b = -3/2, phi = 3/2, y = -3/2} Result: 1.606105802 Test Values: {b = -3/2, phi = 3/2, y = 3/2} ... skip entries to safe data	Failed [108 / 108] Result: -1.3938941974984456 Test Values: {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 1.5]} Result: -0.18362615716444086 Test Values: {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 0.5]} ... skip entries to safe data
19.30.E2	${\displaystyle{\displaystyle s=a\int_{0}^{\phi}\sqrt{1-k^{2}{\sin^{2}}\theta}\mathrm{d}\theta}}$ s = a\int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}		s = a*int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi)	s == a*Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.30.E3	${\displaystyle{\displaystyle s/a=E\left(\phi,k\right)}}$ s/a = \incellintEk@{\phi}{k}		s/a = EllipticE(sin(phi), k)	s/a == EllipticE[\[Phi], (k)^2]	Failure	Failure	Failed [300 / 300] Result: .1410196655-.3375964631*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 1} Result: -.36391978e-1+.5433649104e-1*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.5672114831419685, -0.22929764467344024] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.5579190406370536, -0.16535187593702125] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30.E3	${\displaystyle{\displaystyle E\left(\phi,k\right)={R_{F}\left(c-1,c-k^{2},c\right)-\tfrac{1}{3}k^{2}R_{D}\left(c-1,c-k^{2},c\right)}}}$ \incellintEk@{\phi}{k} = {\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}}		Error	EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2))	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [180 / 180] Result: Complex[3.5743811704478246, 0.7698502565730785] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[3.9424508382496875, -1.017653751864599] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30#Ex3	${\displaystyle{\displaystyle k^{2}=1-(b^{2}/a^{2})}}$ k^{2} = 1-(b^{2}/a^{2})		(k)^(2) = 1 -((b)^(2)/(a)^(2))	(k)^(2) == 1 -((b)^(2)/(a)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30#Ex4	${\displaystyle{\displaystyle c={\csc^{2}}\phi}}$ c = \csc^{2}@@{\phi}		c = (csc(phi))^(2)	c == (Csc[\[Phi]])^(2)	Failure	Failure	Failed [60 / 60] Result: -2.359812877+.7993130071*I Test Values: {c = -3/2, phi = 1/2*3^(1/2)+1/2*I} Result: -1.296085040-.8173084059*I Test Values: {c = -3/2, phi = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [60 / 60] Result: Complex[-3.841312467237177, 3.4490957612740374] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.17530792640393877, -3.4502399957777015] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle L(a,b)=4aE\left(k\right)}}$ L(a,b) = 4a\compellintEk@{k}		L(a , b) = 4*a*EllipticE(k)	L[a , b] == 4*a*EllipticE[(k)^2]	Failure	Failure	Failed [300 / 300] Result: (.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+6.000000000 Test Values: {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 1} Result: (.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+2.437793319+8.063125386*I Test Values: {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 2} ... skip entries to safe data	Error
19.30.E5	${\displaystyle{\displaystyle 4aE\left(k\right)=8aR_{G}\left(0,b^{2}/a^{2},1\right)}}$ 4a\compellintEk@{k} = 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1}		Error	4*a*EllipticE[(k)^2] == 8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [108 / 108] Result: 12.849555921538759 Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1]} Result: Complex[16.411762602778996, -8.063125388322588] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle 8aR_{G}\left(0,b^{2}/a^{2},1\right)=8R_{G}\left(0,a^{2},b^{2}\right)}}$ 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1} = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}		Error	8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) == 8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [18 / 36] Result: -37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, -1.5]} Result: -37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, 1.5]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle 8R_{G}\left(0,a^{2},b^{2}\right)=8abR_{G}\left(0,a^{-2},b^{-2}\right)}}$ 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}} = 8ab\CarlsonsymellintRG@{0}{a^{-2}}{b^{-2}}		Error	8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) == 8*a*b*Sqrt[(b)^(- 2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(- 2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(- 2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(- 2)]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [18 / 36] Result: 37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, 1.5]} Result: 26.729786441110512 Test Values: {Rule[a, -1.5], Rule[b, 0.5]} ... skip entries to safe data
19.30.E6	${\displaystyle{\displaystyle\frac{\partial s}{\partial(1/k)}=\sqrt{a^{2}-b^{2}}F\left(\phi,k\right)}}$ \pderiv{s}{(1/k)} = \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k}	${\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda),c={\csc^{2}}\phi}}$	subs( temp=(1/k), diff( s, temp$(1) ) ) = sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k)	(D[s, {temp, 1}]/.temp-> (1/k)) == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2]	Failure	Failure	Successful [Tested: 300]	Failed [20 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, -2]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, 2]} ... skip entries to safe data
19.30.E6	${\displaystyle{\displaystyle\sqrt{a^{2}-b^{2}}F\left(\phi,k\right)=\sqrt{a^{2}-b^{2}}R_{F}\left(c-1,c-k^{2},c\right)}}$ \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k} = \sqrt{a^{2}-b^{2}}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}	${\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda),c={\csc^{2}}\phi}}$	sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) = sqrt((a)^(2)- (b)^(2))*0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity)	Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]	Error	Failure	Skip - symbolical successful subtest	Skip - No test values generated
19.30#Ex5	${\displaystyle{\displaystyle x=a\sqrt{t+1}}}$ x = a\sqrt{t+1}		x = a*sqrt(t + 1)	x == a*Sqrt[t + 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30#Ex6	${\displaystyle{\displaystyle y=b\sqrt{t}}}$ y = b\sqrt{t}		y = b*sqrt(t)	y == b*Sqrt[t]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30.E8	${\displaystyle{\displaystyle s=\frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\mathrm{d}t}}$ s = \frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\diff{t}		s = (1)/(2)*int(sqrt((((a)^(2)+ (b)^(2))*t + (b)^(2))/(t*(t + 1))), t = 0..(y)^(2)/(b)^(2))	s == Divide[1,2]*Integrate[Sqrt[Divide[((a)^(2)+ (b)^(2))*t + (b)^(2),t*(t + 1)]], {t, 0, (y)^(2)/(b)^(2)}, GenerateConditions->None]	Failure	Aborted	Failed [300 / 300] Result: -3.149531120 Test Values: {a = -3/2, b = -3/2, s = -3/2, y = -3/2} Result: -3.149531120 Test Values: {a = -3/2, b = -3/2, s = -3/2, y = 3/2} ... skip entries to safe data	Skipped - Because timed out
19.30.E9	${\displaystyle{\displaystyle s=\tfrac{1}{2}I(\mathbf{e}_{1})}}$ s = \tfrac{1}{2}I(\mathbf{e}_{1})	${\displaystyle{\displaystyle r=b^{4}/y^{2}}}$	s = (1)/(2)*I(e[1])	s == Divide[1,2]*I[Subscript[e, 1]]	Failure	Failure	Failed [298 / 300] Result: -1.750000000-.4330127020*I Test Values: {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = 1/2*3^(1/2)+1/2*I} Result: -1.066987298-.2500000002*I Test Values: {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [180 / 180] Result: Complex[-1.375, -0.21650635094610968] Test Values: {Rule[Complex[0, 1], 1], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.375, -0.21650635094610968] Test Values: {Rule[Complex[0, 1], 2], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30.E9	${\displaystyle{\displaystyle\tfrac{1}{2}I(\mathbf{e}_{1})=-\tfrac{1}{3}a^{2}b^{2}R_{D}\left(r,r+b^{2}+a^{2},r+b^{2}\right)+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{2}}}}}$ \tfrac{1}{2}I(\mathbf{e}_{1}) = -\tfrac{1}{3}a^{2}b^{2}\CarlsonsymellintRD@{r}{r+b^{2}+a^{2}}{r+b^{2}}+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{2}}}	${\displaystyle{\displaystyle r=b^{4}/y^{2}}}$	Error	Divide[1,2]*I[Subscript[e, 1]] == -Divide[1,3]*(a)^(2)* (b)^(2)* 3*(EllipticF[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)]-EllipticE[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)])/((r + (b)^(2)-r + (b)^(2)+ (a)^(2))*(r + (b)^(2)-r)^(1/2))+ y*Sqrt[Divide[r + (b)^(2)+ (a)^(2),r + (b)^(2)]]	Missing Macro Error	Failure	Skip - symbolical successful subtest	Skip - No test values generated
19.30.E10	${\displaystyle{\displaystyle r^{2}=2a^{2}\cos\left(2\theta\right)}}$ r^{2} = 2a^{2}\cos@{2\theta}	${\displaystyle{\displaystyle 0\leq\theta,\theta\leq 2\pi}}$	(r)^(2) = 2*(a)^(2)* cos(2*theta)	(r)^(2) == 2*(a)^(2)* Cos[2*\[Theta]]	Failure	Failure	Failed [108 / 108] Result: 6.704966234 Test Values: {a = -3/2, r = -3/2, theta = 3/2} Result: -.181360376 Test Values: {a = -3/2, r = -3/2, theta = 1/2} ... skip entries to safe data	Failed [108 / 108] Result: 6.704966234702004 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 1.5]} Result: -0.18136037640662916 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 0.5]} ... skip entries to safe data
19.30.E11	${\displaystyle{\displaystyle s=2a^{2}\int_{0}^{r}\frac{\mathrm{d}t}{\sqrt{4a^{4}-t^{4}}}}}$ s = 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}}	${\displaystyle{\displaystyle q=2a^{2}/r^{2},2a^{2}/r^{2}=\sec\left(2\theta\right)}}$	s = 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r)	s == 2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None]	Error	Failure	-	Failed [208 / 216] Result: 0.042085201578189846 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[s, -1.5]} Result: 3.04208520157819 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[s, 1.5]} ... skip entries to safe data
19.30.E11	${\displaystyle{\displaystyle 2a^{2}\int_{0}^{r}\frac{\mathrm{d}t}{\sqrt{4a^{4}-t^{4}}}=\sqrt{2a^{2}}R_{F}\left(q-1,q,q+1\right)}}$ 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}} = \sqrt{2a^{2}}\CarlsonsymellintRF@{q-1}{q}{q+1}	${\displaystyle{\displaystyle q=2a^{2}/r^{2},2a^{2}/r^{2}=\sec\left(2\theta\right)}}$	2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) = sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+q - 1)*sqrt(t+q)*sqrt(t+q + 1)), t = 0..infinity)	2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] == Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[q - 1/q + 1]],(q + 1-q)/(q + 1-q - 1)]/Sqrt[q + 1-q - 1]	Error	Failure	-	Failed [12 / 12] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[q, 2], Rule[r, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[q, 2], Rule[r, 1.5]} ... skip entries to safe data
19.30.E12	${\displaystyle{\displaystyle s=aF\left(\phi,1/\sqrt{2}\right)}}$ s = a\incellintFk@{\phi}{1/\sqrt{2}}	${\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)},\operatorname{arcsin}\sqrt{2/(q+1)}=\operatorname{arccos}\left(\tan\theta\right)}}$	s = a*EllipticF(sin(phi), 1/(sqrt(2)))	s == a*EllipticF[\[Phi], (1/(Sqrt[2]))^2]	Failure	Failure	Failed [300 / 300] Result: -.201379324+.8785912788*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2} Result: 2.798620676+.8785912788*I Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = 3/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.8505476575870029, 0.390685462269601] Test Values: {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.859414812385125, 0.6494166239344216] Test Values: {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E13	${\displaystyle{\displaystyle P=4\sqrt{2a^{2}}R_{F}\left(0,1,2\right)}}$ P = 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2}		P = 4*sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity)	P == 4*Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0]	Failure	Failure	Failed [60 / 60] Result: -10.25842266+.5000000000*I Test Values: {P = 1/2*3^(1/2)+1/2*I, a = -3/2} Result: -10.25842266+.5000000000*I Test Values: {P = 1/2*3^(1/2)+1/2*I, a = 3/2} ... skip entries to safe data	Failed [60 / 60] Result: Complex[-10.691435361916012, 0.24999999999999997] Test Values: {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-11.37444806380823, 0.43301270189221935] Test Values: {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E13	${\displaystyle{\displaystyle 4\sqrt{2a^{2}}R_{F}\left(0,1,2\right)=\sqrt{2a^{2}}\times 5.24411\;51\ldots}}$ 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2} = \sqrt{2a^{2}}\times 5.24411\;51\ldots		4*sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity) = sqrt(2*(a)^(2)) * 5.2441151	4*Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] == Sqrt[2*(a)^(2)] * 5.2441151	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
19.30.E13	${\displaystyle{\displaystyle\sqrt{2a^{2}}\times 5.24411\;51\ldots=4aK\left(1/\sqrt{2}\right)}}$ \sqrt{2a^{2}}\times 5.24411\;51\ldots = 4a\compellintKk@{1/\sqrt{2}}		sqrt(2*(a)^(2)) * 5.2441151 = 4*a*EllipticK(1/(sqrt(2)))	Sqrt[2*(a)^(2)] * 5.2441151 == 4*a*EllipticK[(1/(Sqrt[2]))^2]	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
19.30.E13	${\displaystyle{\displaystyle 4aK\left(1/\sqrt{2}\right)=a\times 7.41629\;87\dots}}$ 4a\compellintKk@{1/\sqrt{2}} = a\times 7.41629\;87\dots		4*a*EllipticK(1/(sqrt(2))) = a * 7.4162987	4*a*EllipticK[(1/(Sqrt[2]))^2] == a * 7.4162987	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest