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Asymptotic Transformations of q-Series

Published online by Cambridge University Press:  20 November 2018

Richard J. McIntosh
Richard J. McIntosh*
Affiliation:
Department of Mathematics and Statistics University of Regina Regina, SK S4S 0A2, e-mail: mcintosh@math.uregina.ca
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Abstract

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For the $q$-series $\sum\nolimits_{n=0}^{\infty }{{{a}^{n}}{{q}^{b{{n}^{2}}+cn}}/}\,{{(q)}_{n}}$ we construct a companion $q$-series such that the asymptotic expansions of their logarithms as $q\,\to \,{{1}^{-}}$ differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new $q$–hypergeometric identity. We give an asymptotic expansion of a general class of $q$-series containing some of Ramanujan's mock theta functions and Selberg's identities.

Keywords

11B6533D1034E0541A60
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 2 , 01 April 1998 , pp. 412 - 425
Copyright
Copyright © Canadian Mathematical Society 1998

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