Generalized Glaisher-Kinkelin constants and Ramanujan summation of series

DOI10.1007/s40993-023-00505-2OpenAlexW4390657444MaRDI QIDQ6148981

Marc-Antoine Coppo

Publication date: 8 February 2024

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-023-00505-2

zbMATH Keywords

Hurwitz zeta functionBendersky-Adamchik constantsBernoulli numbers of second kindRamanujan summation of seriesBendersky's generalized gamma functions

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Other Dirichlet series and zeta functions (11M41)

Cites Work

• A new class of identities involving Cauchy numbers, harmonic numbers and zeta values
• On shifted Mascheroni series and hyperharmonic numbers
• The generalized-Euler-constant function \(\gamma (z)\) and a generalization of Somos's quadratic recurrence constant
• Polygamma functions of negative order
• Some asymptotic expansions on hyperfactorial functions and generalized Glaisher-Kinkelin constants
• Ramanujan summation of divergent series
• Closed-form calculation of infinite products of Glaisher-type related to Dirichlet series
• Generalized Kinkelin's formulas
• A note on some alternating series involving zeta and multiple zeta values
• On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
• Number Theory

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