An asymptotic form for the Stieltjes constants 𝛾_{𝑘}(𝑎) and for a sum 𝑆ᵧ(𝑛) appearing under the Li criterion

DOI10.1090/S0025-5718-2011-02497-XzbMath1252.11065OpenAlexW2907372031MaRDI QIDQ3094287

Mark W. Coffey, Charles Knessl

Publication date: 24 October 2011

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-2011-02497-x

zbMATH Keywords

Hurwitz zeta functionRiemann zeta functionStieltjes constantsRiemann hypothesisLaurent expansionasymptotic formLi criterion

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Hurwitz and Lerch zeta functions (11M35) Asymptotic representations in the complex plane (30E15)

Related Items (11)

Functional equations for the Stieltjes constants ⋮ Estimates of generalized Stieltjes constants with a quasi-geometric rate of decay ⋮ Explicit upper bounds for the Stieltjes constants ⋮ Series representations for the Stieltjes constants ⋮ Fast computation of the Stieltjes constants ⋮ A non-recursive formula for the higher derivatives of the Hurwitz zeta function ⋮ Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only ⋮ Unnamed Item ⋮ Hypergeometric summation representations of the Stieltjes constants ⋮ Rigorous high-precision computation of the Hurwitz zeta function and its derivatives ⋮ Integral and series representations of the digamma and polygamma functions

Uses Software

• DLMF

Cites Work

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• Power Series Expansions of Riemann's ζ Function
• Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants
• Asymptotic Forms for Laguerre Polynomials

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