Table of Integrals
A. Dieckmann, Physikalisches Institut der Uni Bonn
This table contains hundreds of expressions: indefinite and definite integrals of elliptic integrals, of square roots, arcustangents and a few more exotic functions. Most of them are not found in Gradsteyn-Ryzhik.
Results may be valid outside of the given region of parameters, but should always be checked numerically!
Indefinite Integrals:
strange connection between EllipticTheta and Elliptic Integrals…
apparently it is not known how to integrate m[q] = InverseEllipticNomeQ[q] over q,
the following expressions have therefore been calculated backwards, that is by differentiating the right side with respect to q :
Inspite of the many singularities of this function at a = c * n they seem to cancel in the definite integral…
Here the result is a threefold sum shown in Mathematica syntax:
KSubsets[aList, k] is in Package DiscreteMath`Combinatorica` and gives a list of all subsets with k elements of aList .
For n=3 the sum is 
.
<<Combinatorica`
