Hypergeometric expressions of $L$-values for a Borweins theta product of weight $3$

Abstract

In this paper, we consider a modular form of weight 3, which is a product of the Borweins theta series, and express its $L$-values at $s=1$, $2$ and $3$ in terms of special values of Kamp\'e de F\'eriet hypergeometric functions, which are two-variable generalization of generalized hypergeometric functions.