A note on modified Hermite matrix polynomials

Volume 22, Issue 4, pp 333--346 http://dx.doi.org/10.22436/jmcs.022.04.03

Publication Date: September 05, 2020 Submission Date: May 27, 2020 Revision Date: June 30, 2020 Accteptance Date: July 23, 2020

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Authors

Virender Singh - Department of Applied Mathematics, Galgotias college of Engineering and Technology, Greater Noida, Uttar Pradesh-201306, India. Mumtaz Ahmad Khan - Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India. Abdul Hakim Khan - Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India. Kottakkaran Sooppy Nisar - Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, Prince Sattam bin Abdulaziz University, 11991, Saudi Arabia.

Abstract

The main aim of this paper is to investigate the modified Hermite matrix polynomials \({_M}\mathscr{H}{_n}{(\zeta_1,\lambda;\mathscr{A})}\) by finding some important results such as generating functions, recurrence relations, Rodrigues formula, orthogonality conditions, expansion formula, integrals, fractional integrals, fractional derivatives and some other properties.

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Keywords

• Gamma matrix function
• hypergeometric matrix function
• three term matrix recurrence relation
• modified Hermite matrix differential equation
• modified Hermite matrix polynomials
• orthogonal matrix polynomials

MSC

•  33C05
•  33C45
•  33C90

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