User:Tohline/Math/EQ EllipticIntegral02
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<math>~\frac{2E(k)}{\pi}</math> |
<math>~=</math> |
<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}{2^7 \cdot 3}\biggr)^2 \frac{k^8}{7} ~-~ \cdots - \biggl[ \frac{(2n-1)!!}{2^n n!} \biggr]^2 \frac{k^{2n}}{2n-1}
~-~ \cdots </math> |
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Gradshteyn & Ryzhik (1965), §8.114.1 |
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