Elliptic Integrals - 19.34 Mutual Inductance of Coaxial Circles

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.34.E1	${\displaystyle{\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos\theta)^{-1/2}\cos\theta\mathrm{d}\theta=2ab\int_{-1}^{1}\frac{t\mathrm{d}t}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}}}$ ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}		a*b*int(((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*cos(theta))^(- 1/2)* cos(theta), theta = 0..2*Pi) = 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1)	a*b*Integrate[((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*Cos[\[Theta]])^(- 1/2)* Cos[\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.34.E1	${\displaystyle{\displaystyle 2ab\int_{-1}^{1}\frac{t\mathrm{d}t}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}=2abI(\mathbf{e}_{5})}}$ 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})		2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) = 2*abI(e[5])	2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None] == 2*abI[Subscript[e, 5]]	Failure	Aborted	Failed [300 / 300] Result: -3.959693187-6.593729744*I Test Values: {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = 1/2*3^(1/2)+1/2*I} Result: 2.187421133-4.946615428*I Test Values: {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
19.34#Ex1	${\displaystyle{\displaystyle a_{3}=h^{2}+a^{2}+b^{2}}}$ a_{3} = h^{2}+a^{2}+b^{2}		a[3] = (h)^(2)+ (a)^(2)+ (b)^(2)	Subscript[a, 3] == (h)^(2)+ (a)^(2)+ (b)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34#Ex2	${\displaystyle{\displaystyle a_{5}=0}}$ a_{5} = 0		a[5] = 0	Subscript[a, 5] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34#Ex3	${\displaystyle{\displaystyle b_{5}=1}}$ b_{5} = 1		b[5] = 1	Subscript[b, 5] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34.E3	${\displaystyle{\displaystyle 2abI(\mathbf{e}_{5})=a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})}}$ 2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})		2*abI(e[5]) = a[3]*I(0)- I(e[3])	2*abI[Subscript[e, 5]] == Subscript[a, 3]*I[0]- I[Subscript[e, 3]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34.E4	${\displaystyle{\displaystyle r_{+}^{2}=a_{3}+2ab}}$ r_{+}^{2} = a_{3}+ 2ab		(r[+])^(2) = a[3]+ 2*a*b	(Subscript[r, +])^(2) == Subscript[a, 3]+ 2*a*b	Skipped - no semantic math	Skipped - no semantic math	-	-