Asymptotic expansions of certain partial theta functions-Reference-Cited by-同舟云学术

Asymptotic expansions of certain partial theta functions

Published:2011-07-07 Issue:11 Volume:139 Page:3779-3788
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Berndt Bruce,Kim Byungchan

Abstract

We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2011-139-11/S0002-9939-2011-11062-1/S0002-9939-2011-11062-1.pdf

Reference10 articles.

1. Encyclopedia of Mathematics and its Applications, Vol. 2;Andrews, George E.,1976

2. Encyclopedia of Mathematics and its Applications;Andrews, George E.,1999

3. 𝑞-series identities and values of certain 𝐿-functions;Andrews, George E.;Duke Math. J.,2001

4. Ramanujan’s Notebooks

5. An asymptotic expansion of Ramanujan;Galway, William F.,1999

Cited by 32 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Arithmetic properties and asymptotic formulae for $$\sigma _o\text {mex}(n)$$ and $$\sigma _e\text {mex}(n)$$;The Ramanujan Journal;2024-06-24

2. Eventual log-concavity of k-rank statistics for integer partitions;Journal of Number Theory;2024-06

3. A domain free of the zeros of the partial theta function;Matematychni Studii;2023-01-16

4. Quantum Computation with Continuous-Variable Systems;Springer Theses;2023

5. On the growth of Artin–Tits monoids and the partial theta function;Journal of Combinatorial Theory, Series A;2022-08