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Certain Supercongruences Deriving from Hypergeometric Series Identities


Affiliations
1 Department of Science and Mathematics, Indian Institute of Information Technology, Guwahati, Bongora, Assam-781015, India
     

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In this paper, we deduce some supercongruences for sums involving third power of certain rising factorials using hypergeometric series identities and evaluations. In particular, we first relate a truncated hypergeometric sum with the coefficients of the modular form of weight 3. Further, we confirm certain supercongruence conjectures related to truncated hypergeometric series.

Keywords

Supercongruences, Hypergeometric Series, p-Adic Gamma Functions.
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  • Certain Supercongruences Deriving from Hypergeometric Series Identities

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Authors

Arijit Jana
Department of Science and Mathematics, Indian Institute of Information Technology, Guwahati, Bongora, Assam-781015, India

Abstract


In this paper, we deduce some supercongruences for sums involving third power of certain rising factorials using hypergeometric series identities and evaluations. In particular, we first relate a truncated hypergeometric sum with the coefficients of the modular form of weight 3. Further, we confirm certain supercongruence conjectures related to truncated hypergeometric series.

Keywords


Supercongruences, Hypergeometric Series, p-Adic Gamma Functions.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F29183