Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae

DOI10.1080/10586458.2004.10504559zbMath1127.11057OpenAlexW2085742045MaRDI QIDQ4663081

Tanguy Rivoal

Publication date: 30 March 2005

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1109106442

zbMATH Keywords

Riemann zeta functiongenerating functionsApéry-like series

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (zeta (s)) and (L(s, chi)) (11M06) Irrationality; linear independence over a field (11J72) Evaluation of number-theoretic constants (11Y60)

Related Items (7)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ Binomial sums involving harmonic numbers ⋮ On one method for fast approximation of zeta constants by rational fractions ⋮ Further Apéry-like series for Riemann zeta function ⋮ A bivariate generating function for zeta values and related supercongruences ⋮ Alternating series of Apéry-type for the Riemann zeta function.

Cites Work

• Letter
• Some new identities for \(\zeta(k)\).
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Généralisation d'une construction de R. Apéry
• Empirically Determined Apéry-Like Formulae for ζ(4n+3)
• La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs
• A new matrix inverse
• Irrationality of infinitely many values of the zeta function at odd integers.

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