Derivation of logarithmic integrals expressed in teams of the Hurwitz zeta function

DOI10.3934/math.2020463zbMath1484.30042OpenAlexW3084734970MaRDI QIDQ2132282

Robert Reynolds, Allan Stauffer

Publication date: 27 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2020463

zbMATH Keywords

Cauchy integrallogarithmic functionEuler's constantdefinite integralCatalan's constantPlanck's lawentries of Gradshteyn and Ryzhikbinethexagammalog gamma

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) (zeta (s)) and (L(s, chi)) (11M06) Meromorphic functions of one complex variable (general theory) (30D30) Hurwitz and Lerch zeta functions (11M35) Representations of entire functions of one complex variable by series and integrals (30D10)

Cites Work

• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• A generalized polygamma function
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