Asymptotic expansions pertaining to the logarithmic series and related trigonometric sums

DOI10.7153/jca-07-11zbMath1412.33037OpenAlexW2564796306MaRDI QIDQ4627790

Panagiotis Andrianesis, George Fikioris

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jca-07-11

zbMATH Keywords

asymptotic expansionsLerch zeta-functionEulerian polynomialstrigonometric sumsLerch's transcendentlogarithmic seriesApostol-Bernoulli numbers

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Other functions defined by series and integrals (33E20) Trigonometric and exponential sums (general theory) (11L03) Hurwitz and Lerch zeta functions (11M35)

Uses Software

• DLMF

Cites Work

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• Some formulas related to Hurwitz-Lerch zeta functions
• Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\)
• The Gibbs- Wilbraham phenomenon: An episode in Fourier analysis
• A new bound for the Fejér-Jackson sum
• Power series and asymptotic series associated with the Lerch zeta-function
• On the Apostol-Bernoulli polynomials
• Large parameter cases of the Gauss hypergeometric function
• Asymptotic expansions of the Hurwitz--Lerch zeta function
• On the Hurwitz-Lerch zeta-function.
• A series transformation formula and related polynomials
• The special functions and their approximations. Vol. I, II
• Asymptotic Approximations of Integrals
• Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS II
• A Review of David Gottlieb’s Work on the Resolution of the Gibbs Phenomenon
• Superdirective-Type Near Fields in the Method of Auxiliary Sources
• On multipliers preserving convergence of trigonometric series almost everywhere
• Derivative Polynomials for tanh, tan, sech and sec in Explicit Form