Tbilisi Mathematical Journal

Laguerre-based Hermite-Bernoulli polynomials associated with bilateral series

Waseem Ahmad Khan, Serkan Araci, Mehmet Acikgoz, and Ayhan Esi

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Abstract

In the paper, we define Laguerre-based Hermite-Bernoulli polynomial with its generating function, and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series associated with the newly introduced generating function. Some of whose special cases are also presented. Relevant connections of some results presented here with those involving simpler known partly unilateral and partly bilateral representations are also obtained.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 2 (2018), 111-121.

Dates
Received: 27 November 2017
Accepted: 18 March 2018
First available in Project Euclid: 20 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1529460026

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials
Secondary: 33C05: Classical hypergeometric functions, $_2F_1$

Keywords
Hermite polynomials Laguerre polynomials Bernoulli polynomials Laguerre based Hermite-Bernoulli polynomials summation formulae bilateral series

Citation

Ahmad Khan, Waseem; Araci, Serkan; Acikgoz, Mehmet; Esi, Ayhan. Laguerre-based Hermite-Bernoulli polynomials associated with bilateral series. Tbilisi Math. J. 11 (2018), no. 2, 111--121. https://projecteuclid.org/euclid.tbilisi/1529460026


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