Article ID: MTJPAM-D-20-00027

Title: Certain Generating Functions for Cigler’s Polynomials


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00027; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 284-296

Document Type: Research Paper

Author(s): Sama Arjika a

aDepartment of Mathematics and Informatics, University of Agadez, Post Box 199, Agadez, Niger. And International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair) University of Abomey-Calavi, Post Box 072, Cotonou 50, Benin

Received: 10 September 2020, Accepted: 28 March 2021, Published: 25 April 2021.

Corresponding Author: Sama Arjika (Email address: rjksama2008@gmail.com)

Full Text: PDF

Abstract

In this paper, we use the homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837–851.] to derive Rogers formulas, extended Rogers formulas and Srivastava-Agarwal type bilinear generating functions for Cigler’s polynomials [J. Difference Equ. Appl. 24 (2018), 479–502.]. Finally, we also derive two interesting transformation formulas between 2Φ1,  2Φ2 and 3Φ2.

Keywords: Basic (or q-) hypergeometric series, Homogeneous q-difference operator, Cigler polynomials, Generating functions, Rogers type formulas, Extended Rogers type formulas, Srivastava-Agarwal type bilinear generating functions

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