Symbolic summation methods and hypergeometric supercongruences

Wang, Chen

doi:10.1016/j.jmaa.2020.124068

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Cited by 8 publications

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References 25 publications

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“…During the past few decades, supercongruences concerning truncated hypergeometric series have been widely studied (cf. [2,8,10,15,16,20,21,22,23]).…”

Section: Introductionmentioning

confidence: 99%

Proof of some supercongruences concerning truncated hypergeometric series

Wang,

2020

Preprint

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“…During the past few decades, supercongruences concerning truncated hypergeometric series have been widely studied (cf. [2,8,10,15,16,20,21,22,23]).…”

Section: Introductionmentioning

confidence: 99%

Proof of some supercongruences concerning truncated hypergeometric series

Wang,

2020

Preprint

Self Cite

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Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

Guo

Schlosser

2020

Constr Approx

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Several new q-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in collaboration with Zudilin. More concretely, the results in this paper include q-analogues of supercongruences (referring to p-adic identities remaining valid for some higher power of p) established by Long, by Long and Ramakrishna, and several other q-supercongruences. The six basic hypergeometric transformation formulas which are made use of are Watson’s transformation, a quadratic transformation of Rahman, a cubic transformation of Gasper and Rahman, a quartic transformation of Gasper and Rahman, a double series transformation of Ismail, Rahman and Suslov, and a new transformation formula for a nonterminating very-well-poised $${}_{12}\phi _{11}$$ 12 ϕ 11 series. Also, the nonterminating q-Dixon summation formula is used. A special case of the new $${}_{12}\phi _{11}$$ 12 ϕ 11 transformation formula is further utilized to obtain a generalization of Rogers’ linearization formula for the continuous q-ultraspherical polynomials.

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Proof of some supercongruences concerning truncated hypergeometric series

Wang

2023

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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Symbolic summation methods and hypergeometric supercongruences

Abstract: In this paper, we mainly prove two conjectural supercongruences of Sun by using the following identity 2020 Mathematics Subject Classification. Primary 33C20, 11A07; Secondary 11B65, 05A10.

Cited by 8 publications

References 25 publications

Proof of some supercongruences concerning truncated hypergeometric series

Proof of some supercongruences concerning truncated hypergeometric series

Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

Proof of some supercongruences concerning truncated hypergeometric series

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