Explicit Formulas for Some Infinite ₃<i>F</i>₂(1)-Series

Abstract

We establish two recurrence relations for some Clausen’s hypergeometric functions with unit argument. We solve them to give the explicit formulas. Additionally, we use the moments of Ramanujan’s generalized elliptic integrals to obtain these recurrence relations.

Keywords

• Clausen’s hypergeometric functions
• elliptic integrals
• moments