Evaluation of integrals with hypergeometric and logarithmic functions

DOI10.1515/MATH-2018-0008zbMath1391.05021OpenAlexW2790599138WikidataQ130191385 ScholiaQ130191385MaRDI QIDQ1643972

Anthony Sofo

Publication date: 20 June 2018

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

Full work available at URL: https://doi.org/10.1515/math-2018-0008

zbMATH Keywords

logarithmic integralRiemann zeta functionintegral representationpolylogarithm functionLerch transcendent function

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Special sequences and polynomials (11B83)

Related Items (3)

Parameterized families of polylog integrals ⋮ Logarithmic integrals with applications to BBP and Euler-type sums ⋮ New interesting Euler sums

Cites Work

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• The Lerch zeta function. III: Polylogarithms and special values
• Euler sums and integrals of polylogarithm functions
• Some summation formulas involving harmonic numbers and generalized harmonic numbers
• New families of alternating harmonic number sums
• Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
• A family of shifted harmonic sums
• A master integral in four parameters
• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• Harmonic numbers at half integer values
• The Lerch zeta function I. Zeta integrals
• The Lerch zeta function II. Analytic continuation
• Values of the polygamma functions at rational arguments

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