Abstract
In this article, the integral transform is used to introduce a new family of extended hybrid Sheffer sequences via generating functions and operational rules. The determinant forms and other properties of these sequences are established using a matrix approach. The correspondingresults for the extended hybrid Appell sequences are also obtained. Certain examples in terms of the members of the extended hybrid Sheffer and Appell sequences are framed. By employing operational rules, the identities involving the Lah, Stirling and Pascal matrices are derived for the aforementioned sequences.
Highlights
Fractional calculus is a branch of mathematics that deals with the real or complex number powers of the differential operator
It is shown in [1] that the exploitation of integral transforms with special polynomials is an effective way to accord with fractional derivatives
The exponential operational rule and generating function of the truncated exponential Sheffer are applied on an integral transform to introduce the extended forms of the hybrid Sheffer sequences
Summary
Fractional calculus is a branch of mathematics that deals with the real or complex number powers of the differential operator It is shown in [1] that the exploitation of integral transforms with special polynomials is an effective way to accord with fractional derivatives. The multi-variable forms of special polynomials are studied in a different way via operational techniques These may help in solving problems in classical and quantum mechanics associated with special functions. The 2-variable truncated exponential polynomials (2VTEP) (of order r) en ( x, y) are defined by the following generating function, series expansion and operational rule The exponential operational rule and generating function of the truncated exponential Sheffer are applied on an integral transform to introduce the extended forms of the hybrid Sheffer sequences. The determinant forms and other properties for these sequences are studied via fractional operators and Riordan matrices
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