Series involving \(\psi(z)\) and \(\zeta(z, s)\) functions and evaluation of integrals

DOI10.1134/S1995080219070102zbMath1425.11035OpenAlexW2966289257MaRDI QIDQ2330221

N. V. Savischenko, Yu. A. Brychkov

Publication date: 25 October 2019

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

Full work available at URL: https://doi.org/10.1134/s1995080219070102

zbMATH Keywords

integralszeta functionEuler numberBernoulli numberseriesBernoulli polynomialpolygamma functionEuler polynomial

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15)

Uses Software

• DLMF

Cites Work

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• Certain classes of series involving the zeta function
• Polygamma functions of negative order
• Summing one- and two-dimensional series related to the Euler series
• Some series of the zeta and related functions
• A restricted Epstein zeta function and the evaluation of some definite integrals

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