User:Tohline/Math/EQ EllipticIntegral04 - Revision history

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<math>~E(\mu)</math>
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<math>~=</math>
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<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')^4
~+~ \frac{1^2\cdot 3^2\cdot 5}{2^2\cdot 4^2\cdot 6}\biggl( \ln \frac{4}{k'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} - \frac{1}{5\cdot 6}\biggr)(k')^6
~+~ \cdots
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[http://www.mathtable.com/gr/ Gradshteyn & Ryzhik (1965)], §8.114.3
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where:   <math>~k^' \equiv (1 - \mu^2)^{1 / 2}</math>
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