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A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES $\boldsymbol F_3$

Part of: Elementary number theory Sequences and sets Basic hypergeometric functions

Published online by Cambridge University Press:  13 July 2022

XIAOXIA WANG Open the ORCID record for XIAOXIA WANG [Opens in a new window]  and
MENGLIN YU
XIAOXIA WANG
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China e-mail: xiaoxiawang@shu.edu
MENGLIN YU*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China
*
e-mail: 99mly99@i.shu.edu.cn
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Abstract

Recently, Lin and Liu [‘Congruences for the truncated Appell series $F_3$ and $F_4$ ’, Integral Transforms Spec. Funct. 31(1) (2020), 10–17] confirmed a supercongruence on the truncated Appell series $F_3$ . Motivated by their work, we give a generalisation of this supercongruence by establishing a q-supercongruence modulo the fourth power of a cyclotomic polynomial.

Keywords

truncated Appell seriescongruenceq-congruencecyclotomic polynomial

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Secondary: 11A07: Congruences; primitive roots; residue systems 11B65: Binomial coefficients; factorials; $q$-identities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 296 - 303
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by Natural Science Foundation of Shanghai (22ZR1424100).

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