Integration involving the complete elliptic integral of the first kind K(k)? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T15:19:39Z http://mathoverflow.net/feeds/question/37191 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37191/integration-involving-the-complete-elliptic-integral-of-the-first-kind-kk Integration involving the complete elliptic integral of the first kind K(k)? Dan 2010-08-30T20:36:11Z 2010-08-31T05:55:28Z <p>Is there any reference showing how to do definite integrals involving the complete elliptic integral of the first kind K(k)? Something like </p> <ol> <li>$\int_0^1 K(k) dk$</li> <li>$\int_0^1 k^nK(k) dk$ </li> <li>$\int_0^1 \frac{K(k)}{1+k} dk$</li> </ol> <p>etc...Thanks a lot.</p>