Rocky Mountain Journal of Mathematics

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

H.M. Srivastava, M. Masjed-Jamei, and M.R. Beyki

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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.

Note

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

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 2 (2019), 681-697.

Dates
Received: 2 August 2018
Revised: 22 August 2018
First available in Project Euclid: 23 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1561318400

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

Mathematical Reviews number (MathSciNet)
MR3973247

Zentralblatt MATH identifier
07079991

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials 11B73: Bell and Stirling numbers
Secondary: 11B83: Special sequences and polynomials 26C05: Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]

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

Citation

Srivastava, H.M.; Masjed-Jamei, M.; Beyki, M.R. Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. Rocky Mountain J. Math. 49 (2019), no. 2, 681--697. doi:10.1216/RMJ-2019-49-2-681. https://projecteuclid.org/euclid.rmjm/1561318400


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