My professor, in class, talked about logarithmic singularity of complete elliptic functions of the first kinds: $$ K(k) =\int_0^{\pi/2} \frac{d\theta}{\sqrt{1-k^2\sin^2\theta}} $$ I want to know a reference (online if possibile) about that subject. Can anyone tell me? thank you very much
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Related, might be helpful as it expresses $K'/K$ with the help of $\log k$. – ccorn Dec 07 '13 at 12:22
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Besides, $K(k)$ is a (complete) elliptic integral, an elliptic function would be something else. – ccorn Dec 07 '13 at 12:36
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These might help.
http://www.mhtlab.uwaterloo.ca/courses/me755/web_chap3.pdf
http://web.mst.edu/~lmhall/SPFNS/sfch3.pdf
In addition you might find some useful information for reference in this book,
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2The first two linked docs do not cover logarithmic singularities, and the third is blocked due to its viewing limit. – ccorn Dec 07 '13 at 12:44