Article
Kyungpook Mathematical Journal 2020; 60(4): 731-752
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
The p-deformed Generalized Humbert Polynomials and Their Properties
Rajesh V. Savalia*, B. I. Dave
Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Changa-388 421, DistAnand, Gujarat, India
Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002, Gujarat, India
e-mail: rajeshsavalia.maths@charusat.ac.in
Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002, Gujarat, India
e-mail: bidavemsu@yahoo.co.in
Received: September 10, 2019; Revised: July 29, 2020; Accepted: August 4, 2020
We introduce the p-deformation of generalized Humbert polynomials. For these polynomials, we derive the differential equation, generating function relations, Fibonacci-type representations, and recurrence relations and state the companion matrix. These properties are illustrated for certain polynomials belonging to p-deformed generalized Humbert polynomials.
Keywords: p-Gamma function, p-Pochhammer symbol, differential equation, generating function relations, mixed relations