Template:Math/EQ EllipticIntegral01

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Revision as of 17:53, 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{2K(k)}{\pi}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 + \biggl( \frac{1}{2} \biggr)^2k^2 + \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 k^4 + \biggl( \frac{1\cdot 3\cdot 5}{2^4\cdot 3}\biggr)^2 k^6 + \biggl( \frac{1\cdot 3\cdot...")

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	$\frac{2 K (k)}{π}$	$=$	$1 + (\frac{1}{2})^{2} k^{2} + (\frac{1 \cdot 3}{2 \cdot 4})^{2} k^{4} + (\frac{1 \cdot 3 \cdot 5}{2^{4} \cdot 3})^{2} k^{6} + (\frac{1 \cdot 3 \cdot 5 \cdot 7}{2^{7} \cdot 3})^{2} k^{8} + \dots + [\frac{(2 n - 1)!!}{2^{n} n!}]^{2} k^{2 n} + \dots$
Gradshteyn & Ryzhik (1965), §8.113.1

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