An expansion formula for q-series and applications

Zhi Guo Liu

doi:10.1023/A:1021306016666

An expansion formula for q-series and applications

Zhi Guo Liu^*

^*Corresponding author for this work

Xinxiang Education College

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

50 Scopus citations

Abstract

In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers - Fine identity, the nonterminating ₆φ ₅ summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.

Original language	English
Pages (from-to)	429-447
Number of pages	19
Journal	Ramanujan Journal
Volume	6
Issue number	4
DOIs	https://doi.org/10.1023/A:1021306016666
State	Published - 2002
Externally published	Yes

Keywords

Andrews' identities
Hecke type series
Q-differential operator
Q-series
Rogers-Fine identity
Watson's q-analog of Whipple's theorem
φ summation formula

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abstract = "In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers - Fine identity, the nonterminating 6φ 5 summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.",

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AB - In this paper the author proves a q-expansion formula which utilizes the Leibniz formula for the q-differential operator. This expansion leads to new proofs of the Rogers - Fine identity, the nonterminating 6φ 5 summation formula, and Watson's q-analog of Whipple's theorem. Andrews' identities for sums of three squares and sums of three triangular numbers are also derived. Other identities of Andrews and new identities for Hecke type series are also discussed.

KW - Andrews' identities

KW - Hecke type series

KW - Q-differential operator

KW - Q-series

KW - Rogers-Fine identity

KW - Watson's q-analog of Whipple's theorem

KW - φ summation formula

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DO - 10.1023/A:1021306016666

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SN - 1382-4090

VL - 6

SP - 429

EP - 447

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 4

ER -

An expansion formula for q-series and applications

Abstract

Keywords

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