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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}}
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)}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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)
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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]
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Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})}
2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) = 2*abI(e[5])
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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]]
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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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = h^{2}+a^{2}+b^{2}}
a_{3} = h^{2}+a^{2}+b^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[3] = (h)^(2)+ (a)^(2)+ (b)^(2) |
Subscript[a, 3] == (h)^(2)+ (a)^(2)+ (b)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{5} = 0}
a_{5} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a[5] = 0 |
Subscript[a, 5] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{5} = 1}
b_{5} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b[5] = 1 |
Subscript[b, 5] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})}
2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{+}^{2} = a_{3}+ 2ab}
r_{+}^{2} = a_{3}+ 2ab |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (r[+])^(2) = a[3]+ 2*a*b |
(Subscript[r, +])^(2) == Subscript[a, 3]+ 2*a*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |