Multiple elliptic integrals and differential equations

Abstract

We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and associated singular values for the complete elliptic integral $\mathbf{K}$ with integrals involving $\mathbf{K}$.

8 pages