Dirichlet series and series with Stirling numbers

DOI10.56754/0719-0646.2501.103arXiv2109.09167MaRDI QIDQ6178178

Khristo N. Boyadzhiev

Publication date: 1 September 2023

Published in: Cubo (Temuco) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.09167

zbMATH Keywords

Catalan numbersharmonic numbersCauchy numbersStirling numbers of the first kindhyperharmonic numberscentral binomial coefficientsderangement numbersseries identities

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Convergence and divergence of series and sequences of functions (40A30) Dirichlet series, exponential series and other series in one complex variable (30B50) Numerical summation of series (65B10) Higher logarithm functions (33B30)

Cites Work

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• On Stirling numbers and Euler sums
• Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• A catalog of interesting Dirichlet series
• The Cauchy numbers
• Interesting Series Involving the Central Binomial Coefficient
• Explicit formulas of sums involving harmonic numbers and Stirling numbers
• New series identities with Cauchy, Stirling, and harmonic numbers, and Laguerre polynomials
• Hypergeometry of the Parbelos

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