Asymptotic expansions of certain partial theta functions

Bruce C. Berndt, Byungchan Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3779-3788
Number of pages10
JournalProceedings of the American Mathematical Society
Volume139
Issue number11
DOIs
StatePublished - Nov 2011

Keywords

  • Asymptotic expansion
  • Dirichlet series associated with a polynomial
  • Euler numbers
  • False theta functions
  • Hermite polynomials
  • Partial theta functions
  • Ramanujan's notebooks
  • Theta functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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