Some expansion formulas for a class of generalized Hurwitz–Lerch Zeta functions

DOI10.1080/10652460600926923zbMath1172.11026OpenAlexW2046948756MaRDI QIDQ3422777

Pin-Yu Wang, Shy-Der Lin, Hari M. Srivastava

Publication date: 14 February 2007

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460600926923

zbMATH Keywords

Hurwitz zeta functionRiemann zeta functionfractional calculusLeibniz ruleRiemann-Liouville fractional derivativeexpansion formulasLerch's functional equationHurwitz-Lerch zeta functionsgeneralized zeta functionFox-Wright generalized hypergeometric functionBernoulli polynomials and Bernoulli numbers of higher orderEulerian integral of the first kindLerch's transformation formulaLipschitz-Lerch zeta functionssum-integral representations

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Fractional derivatives and integrals (26A33) Classical hypergeometric functions, ({}_2F_1) (33C05) Hurwitz and Lerch zeta functions (11M35)

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Cites Work

• An explicit formula for the generalized Bernoulli polynomials
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Remarks on some relationships between the Bernoulli and Euler polynomials.
• Some families of the Hurwitz-Lerch zeta functions and associated fractional derivative and other integral representations
• The special functions and their approximations. Vol. I, II
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
• A certain class of generating functions involving bilateral series
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