Hypergeometric summation representations of the Stieltjes constants

DOI10.1524/ANLY.2013.1160zbMath1284.11118arXiv1106.5148OpenAlexW2964288805MaRDI QIDQ2841425

Mark W. Coffey

Publication date: 25 July 2013

Published in: Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5148

zbMATH Keywords

cosine integralsine integralHurwitz zeta functionRiemann zeta functionStieltjes constantsintegral representationgeneralized hypergeometric functionseries representationGamma functiondigamma functionEuler constant

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Hurwitz and Lerch zeta functions (11M35) Evaluation of number-theoretic constants (11Y60)

Related Items (9)

Functional equations for the Stieltjes constants ⋮ Explicit upper bounds for the Stieltjes constants ⋮ On the Stieltjes constants with respect to harmonic zeta functions ⋮ The signs of the Stieltjes constants associated with the Dedekind zeta function ⋮ Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function ⋮ Applications of the Laurent-Stieltjes constants for Dirichlet \(L\)-series ⋮ Fast computation of the Stieltjes constants ⋮ Stieltjes constants of \(L\)-functions in the extended Selberg class ⋮ On the Stieltjes constants and gamma functions with respect to alternating Hurwitz zeta functions

Cites Work

• On representations and differences of Stieltjes coefficients, and other relations
• New results on the Stieltjes constants: asymptotic and exact evaluation
• Addison-type series representation for the Stieltjes constants
• On the power series coefficients of the Riemann zeta function
• On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams
• An asymptotic form for the Stieltjes constants 𝛾_{𝑘}(𝑎) and for a sum 𝑆ᵧ(𝑛) appearing under the Li criterion
• Integral and series representations of the digamma and polygamma functions
• On the Hurwitz zeta-function

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