On local solutions of the Ramanujan equation and their connection formulae

Abstract

We show connection formulae of local solutions of the Ramanujan equation between the origin and the infinity. These solutions are given by the Ramanujan function, the $q$-Airy function and the divergent basic hypergeometric series ${}_2{\phi }_0(0,0;-;q,x)$. We use two different $q$-Borel-Laplace transformations to obtain our connection formulae.

arXiv admin note: text overlap with arXiv:1104.0755

References in corpus (3)

• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• Algebraic construction of the Stokes sheaf for irregular linear q-difference equations
• A unified approach to $q$-special functions of the Laplace type

Cited by in corpus (1)

• Asymptotic formulae of two divergent bilateral basic hypergeometric series