Spherical Couplings and Multiple Elliptic Integrals

TL;DR

This paper explores the evaluation of elliptic integrals as couplings on spheres, providing new integral and series representations for mathematical constants like pi, G, and zeta(3).

Contribution

It introduces a novel approach to express elliptic integrals as spherical couplings, leading to new representations of key mathematical constants.

Findings

Derived new integral representations for pi, G, and zeta(3).

Established series expansions related to elliptic integrals on spheres.

Connected elliptic integrals with spherical couplings in a novel way.

Abstract

Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.