Congruences arising from Apéry-type series for zeta values

DOI10.1016/j.aam.2012.05.003zbMath1293.11030arXiv1108.1893OpenAlexW2029396671MaRDI QIDQ1761470

Tatiana Hessami Pilehrood, Khodabakhsh Hessami Pilehrood

Publication date: 15 November 2012

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.1893

zbMATH Keywords

Bernoulli numbercongruencecreative telescopingzeta valuemultiple harmonic sumWZ pairApéry-like seriesfinite central binomial sumzeta value congruence

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Congruences; primitive roots; residue systems (11A07) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

From generating series to polynomial congruences ⋮ On a sequence transformation with integral coefficients for Euler's constant. II. ⋮ Proof of some supercongruences concerning truncated hypergeometric series ⋮ New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series ⋮ Congruences for central binomial sums and finite polylogarithms ⋮ A bivariate generating function for zeta values and related supercongruences ⋮ Two congruences concerning Apéry numbers conjectured by Z.-W. Sun ⋮ Series representing transcendental numbers that are not U-numbers

Cites Work

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• Some new identities for \(\zeta(k)\).
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• Congruences concerning Bernoulli numbers and Bernoulli polynomials
• Congruences for central binomial sums and finite polylogarithms
• Super congruences and Euler numbers
• Central Binomial Sums, Multiple Clausen Values, and Zeta Values
• Congruences of alternating multiple harmonic sums
• A generalization of a curious congruence on harmonic sums
• Experimental Determination of Apéry-like Identities for ς(2n + 2)
• WOLSTENHOLME TYPE THEOREM FOR MULTIPLE HARMONIC SUMS

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