Semi-automated proof of supercongruences on partial sums of hypergeometric series

DOI10.1016/j.jsc.2018.06.004zbMath1418.68248OpenAlexW2808728538MaRDI QIDQ1733315

Ji-Cai Liu

Publication date: 21 March 2019

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2018.06.004

zbMATH Keywords

combinatorial identitiesEuler numberssupercongruencesharmonic numbers

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Number-theoretic algorithms; complexity (11Y16) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (19)

Proof of some conjectural supercongruences of Guo and Schlosser ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Supercongruences for sums involving fourth power of some rising factorials ⋮ Polynomial reduction and supercongruences ⋮ Proof of a generalization of the (C.2) supercongruence of Van Hamme ⋮ PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS ⋮ Congruences corresponding to hypergeometric identities. I: \(_2F_1\) transformations ⋮ Supercongruences for sums involving Domb numbers ⋮ Congruences for the truncated Appell series F₃ and F₄ ⋮ Some congruences related to a congruence of Van Hamme ⋮ On two supercongruences for sums of Apéry-like numbers ⋮ Proof of a generalization of the (B.2) supercongruence of Van Hamme through a \(q\)-microscope ⋮ Supercongruences for sums involving rising factorial ⋮ Some supercongruences arising from symbolic summation ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Supercongruences concerning truncated hypergeometric series ⋮ Proof of Sun's conjectural supercongruence involving Catalan numbers ⋮ On two supercongruences involving Almkvist-Zudilin sequences ⋮ Ramanujan-type supercongruences involving Almkvist-Zudilin numbers

Uses Software

• SIGMA

Cites Work

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• Hypergeometric evaluation identities and supercongruences
• Ramanujan-type supercongruences
• Super congruences and Euler numbers
• A refinement of a congruence result by van Hamme and Mortenson
• Symbolic summation assists combinatorics
• Gaussian Hypergeometric series and supercongruences
• A $p$-adic supercongruence conjecture of van Hamme
• Some generalizations of a supercongruence of van Hamme

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