On new extensions of the generalized Hermite matrix polynomials

  • Ayman Shehata Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt; Department of Mathematics, College of Science and Arts, Un-aizah, Qassim University, Qassim, Kingdom of Saudi Arabia
Keywords: matrix functional calculus, Hermite matrix polynomials, Hermite matrix differential equation, fractional integrals, fractional derivatives


Various families of generating matrix functions have been established in diverse ways. The objective of the present paper is to investigate these generalized Hermite matrix polynomials, and derive some important results for them, such as, the generating matrix functions, matrix recurrence relations, an expansion of xnI, finite summation formulas, addition theorems, integral representations, fractional calculus operators, and certain other implicit summation formulae.


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