The Lerch transcendent from the point of view of Fourier analysis

DOI10.1016/j.jmaa.2015.05.048zbMath1321.11093OpenAlexW432010140MaRDI QIDQ2352183

Luis M. Navas, Juan Luis Varona, Francisco J. Ruiz

Publication date: 30 June 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.05.048

zbMATH Keywords

Fourier seriesHurwitz zeta functionsBernoulli polynomialsconjugate Fourier seriesLerch transcendent function

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Hurwitz and Lerch zeta functions (11M35)

Related Items (3)

A note on Appell sequences, Mellin transforms and Fourier series ⋮ MULTIPLICATION FORMULA AND (w, q)-ALTERNATING POWER SUMS OF TWISTED q-EULER POLYNOMIALS OF THE SECOND KIND ⋮ Real zeros of Hurwitz-Lerch zeta functions in the interval \((-1,0)\)

Cites Work

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• Asymptotic behavior of the Lerch transcendent function
• The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials
• Old and new identities for Bernoulli polynomials via Fourier series
• Möbius inversion formulas for flows of arithmetic semigroups
• On the Lerch zeta function
• Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
• Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers
• Polynomial interpolation and asymptotic representations for zeta functions
• Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function

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