Integrals of $K$ and $E$ from Lattice Sums

J. G. Wan; I. J. Zucker

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arXiv · 1410.7081

Integrals of $K$ and $E$ from Lattice Sums

J. G. Wan·I. J. Zucker

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Abstract

We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals $K$ and $E$. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced.

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BibTeX RIS

J. G. Wan, I. J. Zucker. 2014-10-26. Integrals of $K$ and $E$ from Lattice Sums. https://arxiv.org/abs/1410.7081

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