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SUMS OF PARTIAL THETA FUNCTIONS THROUGH AN EXTENDED BAILEY TRANSFORM

Part of: Basic hypergeometric functions Combinatorics Additive number theory; partitions

Published online by Cambridge University Press:  13 May 2020

MOHAMED EL BACHRAOUI Open the ORCID record for MOHAMED EL BACHRAOUI [Opens in a new window]
MOHAMED EL BACHRAOUI*
Affiliation:
Department of Mathematical Sciences, United Arab Emirates University, PO Box 15551, Al-Ain, UAE email melbachraoui@uaeu.ac.ae
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Abstract

In this note, we evaluate sums of partial theta functions. Our main tool is an application of an extended version of the Bailey transform to an identity of Gasper and Rahman on $q$-hypergeometric series.

Keywords

partial theta functionsBailey transformq-seriesbasic hypergeometric series

MSC classification

Primary: 05A30: $q$-calculus and related topics
Secondary: 11P84: Partition identities; identities of Rogers-Ramanujan type 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 1 - 10
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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