A connection formula between the Ramanujan function and the $q$-Airy function
Classical Analysis and ODEs
2011-07-04 v2
Abstract
We show a connection formula between two different -Airy functions. One is called the Ramanujan function which appears in Ramanujan's "Lost notebook". Another one is called the -Airy function that obtained in the study of the second -Painlev\'e equation. We use the -Borel transformation and the -Laplace transformation following C. Zhang to obtain the connection formula.
Keywords
Cite
@article{arxiv.1104.0755,
title = {A connection formula between the Ramanujan function and the $q$-Airy function},
author = {Takeshi Morita},
journal= {arXiv preprint arXiv:1104.0755},
year = {2011}
}