On The Chaotic Asymptotics of Ramanujan's Entire Function $A_q(z)$

Details On The Chaotic Asymptotics of Ramanujan's Entire Function $A_q(z)$ On The Chaotic Asymptotics of Ramanujan's Entire Function $A_q(z)$

2006-11-08

arxiv.org/abs/math/0611211v1

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

We will use a discrete analogue of the classical \emph{Laplace} method to show that for infinitely many positive integers $n$, the main term of the asymptotic expansions of scaled confluent basic hypergeometric functions, including the Ramanujan's entire function $A_{q}(z)$, could be expressed in $\theta$-functions, and the error term depends on the ergodic property of certain real scaling parameter.

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