New $ q $-supercongruences arising from a summation of basic hypergeometric series

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-a...

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Veröffentlicht in:AIMS mathematics 2022, Vol.7 (3), p.4125-4136
Hauptverfasser: Wei, Chuanan, Li, Chun
Format: Artikel
Sprache:eng
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Zusammenfassung:With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-analogue of a formula due to Liu [14 ] .
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022228