A connection formula between the Ramanujan function and the $q$-Airy function

Abstract

We show a connection formula between two different $q$-Airy functions. One is called the Ramanujan function which appears in Ramanujan's "Lost notebook". Another one is called the $q$-Airy function that obtained in the study of the second $q$-Painlevé equation. We use the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula.

References in corpus (2)

• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• A unified approach to $q$-special functions of the Laplace type

Cited by in corpus (1)

• A unified approach to $q$-special functions of the Laplace type