User:Tohline/Math/EllipticIntegral01

From VistrailsWiki
< User:Tohline
Revision as of 21:57, 15 July 2020 by Tohline (talk | contribs) (Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="center" colspan="3"> … of the First Kind </td> </tr> <tr> <td align="right"> <math>~\frac{2K(k)}{\…')
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

… of the First Kind

<math>~\frac{2K(k)}{\pi}</math>

<math>~=</math>

<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 5 \cdot 7}{2^7 \cdot 3}\biggr)^2 k^8 + \cdots + \biggl[ \frac{(2n-1)!!}{2^n n!} \biggr]^2 k^{2n} + \cdots </math>

§8.113 and §8.114 of Gradshteyn & Ryzhik (1965), §8.113