Asymptotic expansions of certain partial theta functions

Bruce C. Berndt; Byungchan Kim

doi:10.1090/S0002-9939-2011-11062-1

Asymptotic expansions of certain partial theta functions

Bruce C. Berndt, Byungchan Kim

School of Natural Sciences

University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

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 language	English
Pages (from-to)	3779-3788
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2011-11062-1
State	Published - 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

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10.1090/S0002-9939-2011-11062-1

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title = "Asymptotic expansions of certain partial theta functions",

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.",

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

author = "Berndt, \{Bruce C.\} and Byungchan Kim",

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AU - Berndt, Bruce C.

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N2 - 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.

AB - 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.

KW - Asymptotic expansion

KW - Dirichlet series associated with a polynomial

KW - Euler numbers

KW - False theta functions

KW - Hermite polynomials

KW - Partial theta functions

KW - Ramanujan's notebooks

KW - Theta functions

UR - https://www.scopus.com/pages/publications/79960777951

U2 - 10.1090/S0002-9939-2011-11062-1

DO - 10.1090/S0002-9939-2011-11062-1

M3 - Article

AN - SCOPUS:79960777951

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SP - 3779

EP - 3788

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Asymptotic expansions of certain partial theta functions

Abstract

Keywords

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