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arXiv · 2403.07298

Multiple elliptic integrals and differential equations

John M. Campbell·M. Lawrence Glasser·Yajun Zhou
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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 $\mathbf K$.

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John M. Campbell, M. Lawrence Glasser, Yajun Zhou. 2024-03-12. Multiple elliptic integrals and differential equations. https://doi.org/10.1080/10652469.2026.2717571

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