The Stokes phenomenon for the $q$-difference equation satisfied by the basic hypergeometric series ${}_3{\phi }_1(a_1,a_2,a_3;b_1;q,x)$

Abstract

We show the connection formula for the basic hypergeometric series ${}_3{\phi }_1(a_1,a_2,a_3;b_1;q,x)$ between around the origin and infinity by the using of the $q$-Borel-Laplace transformations. We also show the limit $q\to 1-0$ of the new connection formula.

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

Cited by in corpus (1)

• The $q$-Borel Sum of Divergent Basic Hypergeometric Series ${}_r{\phi }_s(a;b;q,x)$