A theta function identity and its implications

Zhi Guo Liu

doi:10.1090/S0002-9947-04-03572-X

A theta function identity and its implications

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

28 Scopus citations

Abstract

In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for ∏_n=1 ^∞(1-qⁿ)¹⁰ is given. The proofs are self-contained and elementary.

Original language	English
Pages (from-to)	825-835
Number of pages	11
Journal	Transactions of the American Mathematical Society
Volume	357
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-04-03572-X
State	Published - Feb 2005

Keywords

Elliptic functions
Infinite products
Theta function identities

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10.1090/S0002-9947-04-03572-X

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abstract = "In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for ∏n=1 ∞(1-qn)10 is given. The proofs are self-contained and elementary.",

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AB - In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for ∏n=1 ∞(1-qn)10 is given. The proofs are self-contained and elementary.

KW - Elliptic functions

KW - Infinite products

KW - Theta function identities

UR - https://www.scopus.com/pages/publications/13844255408

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ER -

A theta function identity and its implications

Abstract

Keywords

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