Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

H.M. Srivastava; M. Masjed-Jamei; M.R. Beyki

doi:10.1216/RMJ-2019-49-2-681

Abstract

By means of six specific generating functions, we introduce a type of generalized parametric Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials and systematically study their basic properties. As an application of the new polynomials, we use them in computing a new series of Taylor-type.

Funding Statement

The second author was supported by the Alexander von Humboldt Foundation, grant No. 3.4-IRN-1128637-GF-E.

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H.M. Srivastava. M. Masjed-Jamei. M.R. Beyki. "Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials." Rocky Mountain J. Math. 49 (2) 681 - 697, 2019. https://doi.org/10.1216/RMJ-2019-49-2-681

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Received: 2 August 2018; Revised: 22 August 2018; Published: 2019

First available in Project Euclid: 23 June 2019

zbMATH: 07079991

MathSciNet: MR3973247

Digital Object Identifier: 10.1216/RMJ-2019-49-2-681

Subjects:

Primary: 11B68 , 11B73

Secondary: 11B83 , 26C05

Keywords: Apostol-Bernoulli polynomials of order $\alpha $ , Apostol-Euler polynomials of order $\alpha $ , Apostol-Genocchi polynomials of order $\alpha $ , Appell polynomials , Chebyshev polynomials of the first and second kind , computation of Taylor type series , generating functions , parametric generalizations

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