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Analytical properties of the generalized heat matrix polynomials associated with fractional calculus. (English) Zbl 1476.33012

Summary: In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties of the generalized heat matrix polynomials are obtained including generating matrix functions, finite sums, and Laplace integral transforms. In addition, further properties are investigated using fractional calculus operators.

MSC:

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
26A33 Fractional derivatives and integrals
44A20 Integral transforms of special functions

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