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!
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 .