Abstract
The paper is an accomplishment of a new 3-variable 4-parameter generating function for Humbert matrix polynomials with an approach of unifying several classes of matrix valued polynomials using standard techniques of series manipulation. The results are contained in the form of explicit expression, hypergeometric matrix representation, generating functions and three additional expansions in nexus with Legendre, Hermite and Gegenbauer polynomials within discrete sections. A range of special cases is evenly traced that accounts due to the genuine wholesome generalization of such matrix polynomials.
Highlights
Special functions of matrices is a prominent topic in the literature of matrix analysis
In [33], Srivastava and Brenner gave bounds for Jacobi and related polynomials derived by matrix methods
Latest innovations in matrix versions for the classical families of orthogonal polynomials such as Jacobi, extended Jacobi, Bessel, Hermite, Laguerre, Gegenbauer, Chebyshev polynomials and some other special functions are introduced by many authors for matrices in CN×N
Summary
Special functions of matrices is a prominent topic in the literature of matrix analysis. Latest innovations in matrix versions for the classical families of orthogonal polynomials such as Jacobi, extended Jacobi, Bessel, Hermite, Laguerre, Gegenbauer, Chebyshev polynomials and some other special functions are introduced by many authors for matrices in CN×N, (see for example [2,3,6,7,8,11,12,13,14,15,16,20,27,28,29,30,31]). Motivated by the above literature, in the present article we give a 3-variable 4parameter matrix generalization for Humbert matrix polynomials PnA,m(x, y, z; a, b, c, d) [3V4PgHMaP] which unifies a number of matrix polynomials in the complex plane CN×N. The 3-variable matrix polynomial PnA,m(x, y, z; a, b, c, d) is exploited for some more generating functions and additional expansions
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