Template:Math/EQ EllipticIntegral02

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Revision as of 17:55, 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>\frac{2E(k)}{\pi}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 - \frac{1}{2^2} ~k^2 - \frac{1^2\cdot 3}{2^2\cdot 4^2}~ k^4 - \biggl(\frac{1\cdot 3\cdot 5}{2^4\cdot 3}\biggr)^2~\frac{ k^6 }{5} - \biggl( \frac{1\cdot 3\cdot 5 \cdot 7}{2^...")

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	$\frac{2 E (k)}{π}$	$=$	$1 - \frac{1}{2^{2}} k^{2} - \frac{1^{2} \cdot 3}{2^{2} \cdot 4^{2}} k^{4} - (\frac{1 \cdot 3 \cdot 5}{2^{4} \cdot 3})^{2} \frac{k^{6}}{5} - (\frac{1 \cdot 3 \cdot 5 \cdot 7}{2^{7} \cdot 3})^{2} \frac{k^{8}}{7} - \dots - [\frac{(2 n - 1)!!}{2^{n} n!}]^{2} \frac{k^{2 n}}{2 n - 1} - \dots$
Gradshteyn & Ryzhik (1965), §8.114.1

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