Certain properties of modified Hermite-type matrix polynomials ∗

M S Metwally; S Abo-Hasha; Karima  Hamza

doi:10.48165/bpas.2023.42E.1.2

Authors

M S Metwally Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Egyp
S Abo-Hasha Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.
Karima Hamza Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.

DOI:

https://doi.org/10.48165/bpas.2023.42E.1.2

Keywords:

Generalized Hermite-type matrix polynomials, Generating matrix func tions, modified Chebyshev, modified Legendre, modified Hermite-Hermite

Abstract

This paper deals with the investigation of an expansion formula, a summa tion formula, a multiplication theorem, an addition theorem, matrix recurrence relations, fractional integrals, fractional derivatives, Laplace transform, Mellin transform and Frac tional Fourier transform for the modified Hermite-type matrix polynomials and some other properties. We also give new definitions for the modified Chebyshev’s-type, the modified Legendre’s-type and the modified Hermite-Hermite-type matrix polynomials by using these polynomials and we further prove some new results and relations.

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