Template:Math/EQ EllipticIntegral04

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Revision as of 17:57, 29 June 2024 by Joel2 (talk | contribs) (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/SpecialFunctions#Complete_Elliptic_Integrals </td> <td align="right"> <math>E(\mu)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 ~+~ \frac{1}{2}\biggl( \ln \frac{4}{k'} - \frac{1}{1\cdot 2}\biggr)(k')^2 ~+~ \frac{1^2\cdot 3}{2^2\cdot 4}\biggl( \ln \frac{4}{k'} - \frac{2}{1\cdot 2} - \frac{1}{3\cdot 4}\biggr)(k')...")
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E(μ)

=

1+12(ln⁡4k′−11⋅2)(k′)2+12⋅322⋅4(ln⁡4k′−21⋅2−13⋅4)(k′)4+12⋅32⋅522⋅42⋅6(ln⁡4k′−21⋅2−23⋅4−15⋅6)(k′)6+⋯

Gradshteyn & Ryzhik (1965), §8.114.3

where:   k'≡(1−μ2)1/2