A new series for π3and related congruences

DOI10.1142/S0129167X1550055XzbMath1321.11023arXiv1009.5375MaRDI QIDQ2943733

Zhi-Wei Sun

Publication date: 4 September 2015

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5375

zbMATH Keywords

central binomial coefficientscongruences modulo prime powersBernoulli and Euler numbersseries for \(\pi^{3}\)

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Congruences; primitive roots; residue systems (11A07) Evaluation of number-theoretic constants (11Y60)

Related Items (21)

Proof of two conjectural supercongruences involving Catalan-Larcombe-French numbers ⋮ Super congruences for two Apéry-like sequences ⋮ On two conjectural congruences of Sun involving harmonic numbers ⋮ Proof of some congruences conjectured by Z.-W. Sun ⋮ Congruences for Apéry numbers βn =∑k=0nn k2n+k k ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ Modulo $p^2$ congruences involving harmonic numbers ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ Supercongruences related to 3F2(1) involving harmonic numbers ⋮ Harmonic-binomial Euler-like sums via expansions of \((\arcsin x)^p\) ⋮ On sums of binomial coefficients involving Catalan and delannoy numbers modulo \(p^2\) ⋮ Some congruences on harmonic numbers and binomial sums ⋮ A further \(q\)-analogue of Van Hamme's (H.2) supercongruence for any prime \(p\equiv 1\pmod{4}\) ⋮ New series involving harmonic numbers and squared central binomial coefficients ⋮ A bivariate generating function for zeta values and related supercongruences ⋮ On some congruences involving Domb numbers and harmonic numbers ⋮ On two conjectural supercongruences of Z.-W. Sun ⋮ TWO SUPERCONGRUENCES RELATED TO MULTIPLE HARMONIC SUMS ⋮ Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ Symbolic summation methods and congruences involving harmonic numbers ⋮ On two supercongruences involving Almkvist-Zudilin sequences

Cites Work

• Unnamed Item
• On congruences related to central binomial coefficients
• On the sum \(\sum_{k\equiv r\pmod m}{n\choose k}\) and related congruences.
• More congruences for central binomial coefficients
• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• New congruences for central binomial coefficients
• Congruences concerning Bernoulli numbers and Bernoulli polynomials
• Super congruences and Euler numbers
• Congruences involving Bernoulli and Euler numbers
• On Wolstenholme's theorem and its converse
• On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson
• On sums of binomial coefficients modulo p²
• Gaussian Hypergeometric series and supercongruences

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