Certain properties of modified Hermite-type matrix polynomials
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Certain properties of modified Hermite-type matrix polynomials
S. Metwally1, S. Abo-Hasha2 and Karima Hamza3
BPAS-E-Math and Stat. Vol.42E(1) June 2023
DOI: 10.48165/bpas.2023.42E.1.
page: 5-26
Description
Description
Certain properties of modified Hermite-type matrix polynomials
- S. Metwally1, S. Abo-Hasha2 and Karima Hamza3
- Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Egypt.
2,3. Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.
- E-mail: met641958@yahoo.com , 2. E-mail: dr.shadyhasha@gmail.com
- E-mail: karimahamza767@gmail.com
Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief).
Received August 11, 2022 / Revised March 17, 2023 / Accepted April 02, 2023. Online First Published
on June 30, 2023 at https://www.bpasjournals.com/.
†Corresponding author Karima Hamza, E-mail: karimahamza767@gmail.com
Abstract
This paper deals with the investigation of an expansion formula, a summation formula, a multiplication theorem, an addition theorem, matrix recurrence relations, fractional integrals, fractional derivatives, Laplace transform, Mellin transform and Fractional 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.
Key words Generalized Hermite-type matrix polynomials, Generating matrix functions, modified Chebyshev, modified Legendre, modified Hermite-Hermite.
2020 Mathematics Subject Classification 33C45, 34A05, 15A60.
