A connection formula of a divergent bilateral basic hypergeometric function

Abstract

We give the new connection formula for the divergent bilateral basic hypergeometric series ${}_2{\psi }_2(a_1,a_2;b_1;q,x)$ by the using of the $q$-Borel-Laplace resummation method and Slater's formula. The connection coefficients are given by elliptic functions.

References in corpus (3)

• A Connection Formula of the Hahn-Exton $q$-Bessel Function
• A Connection Formula for the $q$-Confluent Hypergeometric Function
• Asymptotic formulae of two divergent bilateral basic hypergeometric series