Ramanujan's "Lost" notebook IX: The partial theta function as an entire function

George E. Andrews

doi:10.1016/j.aim.2004.03.013

Ramanujan's "Lost" notebook IX: The partial theta function as an entire function

George E. Andrews

Mathematics

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

18 Scopus citations

Abstract

We establish the infinite product expansion for ∑_n≥0aⁿqⁿ². This is a corrected version of theexpansion stated in Ramanujan's "Lost" Notebook. The proof requires the study of a newfamily of polynomials which while not orthogonal have many similar properties.

Original language	English (US)
Pages (from-to)	408-422
Number of pages	15
Journal	Advances in Mathematics
Volume	191
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2004.03.013
State	Published - Mar 1 2005

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2004.03.013

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title = "Ramanujan's {"}Lost{"} notebook IX: The partial theta function as an entire function",

abstract = "We establish the infinite product expansion for ∑n≥0anqn2. This is a corrected version of theexpansion stated in Ramanujan's {"}Lost{"} Notebook. The proof requires the study of a newfamily of polynomials which while not orthogonal have many similar properties.",

author = "Andrews, \{George E.\}",

note = "Funding Information: *Tel.: 814-865-6642; fax: 814-865-3735. E-mail address: [email protected]. 1Partially supported by National Science Foundation Grant DMS-0200047.",

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N2 - We establish the infinite product expansion for ∑n≥0anqn2. This is a corrected version of theexpansion stated in Ramanujan's "Lost" Notebook. The proof requires the study of a newfamily of polynomials which while not orthogonal have many similar properties.

AB - We establish the infinite product expansion for ∑n≥0anqn2. This is a corrected version of theexpansion stated in Ramanujan's "Lost" Notebook. The proof requires the study of a newfamily of polynomials which while not orthogonal have many similar properties.

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JO - Advances in Mathematics

JF - Advances in Mathematics

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Ramanujan's "Lost" notebook IX: The partial theta function as an entire function

Abstract

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