Certain results on generalized Humbert-Hermite polynomials

ABSTRACT

In this article, we introduce a new class of generalized Humbert-Hermite polynomials of two variables. We are conscious that the present paper was inspired by a unified presentation of a class of two-variable Humbert’s polynomials that generalize the well-known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjevi’c, Gould, Milovanovi’c and Djordjevi’c, Pathan, and Khan polynomials. Also, we present well-known results by analyzing the particular values of the parameter. We give the surface representation of a generalized Humbert-Hermite polynomial using some particular values of the parameters.

KEYWORDS:

• Hermite polynomials
• Humbert polynomials
• Gegenbauer polynomials
• Chebyshev polynomials
• Pathan-khan polynomials
• hypergeometric function

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Nabiullah Khan

Nabiullah Khan is a Professor at the Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh. His research interest includes applicable analysis, Special functions especially generating functions and integral transform. He completed his M.Phil and Ph.D. in the years 1998 and 2002 from Aligarh Muslim University. He has more than 100 research article in reputed national and international journals.

Mohammad Iqbal Khan

Mohammad Iqbal Khan is pursuing Ph.D from Department of Applied Mathematics, Faculty of Engineering and Technology at Aligarh Muslim University, Aligarh.

Saddam Husain

Saddam Husain is submitted their Ph.D thesis under the supervision of Prof. Nabiullah Khan at the Department of Applied Mathematics, Faculty of Engineering and Technology at Aligarh Muslim University, Aligarh. His research interest includes applicable analysis, Special functions especially generating functions and integral transform. He has published 14 research article and 8 are communicated in national and international SCI and Scopus journals.

Mohd Asif Shah

Mohd Asif Shah is associated professor at Department of Economics, Kebri Dehar University, Kebri Dehar, Ethiopia. He has published more than 100 research article in national and international reputed journals.