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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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

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

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

Permanent link to this document

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

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


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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