Geodesic
Asymptotic Transformations of q-Series
Canadian journal of mathematics, Tome 50 (1998) no. 2, pp. 412-425

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1998-022-x
Mots-clés : 11B65, 33D10, 34E05, 41A60 
McIntosh, Richard J. Asymptotic Transformations of q-Series. Canadian journal of mathematics, Tome 50 (1998) no. 2, pp. 412-425. doi: 10.4153/CJM-1998-022-x
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