Some properties of Hermite-based Sheffer polynomials

In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite–Sheffer polynomials are considered. Further, an operational formalism providing a correspondence bet...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-11, Vol.217 (5), p.2169-2183
Main Authors: Khan, Subuhi, Walid Al-Saad, Mustafa, Yasmin, Ghazala
Format: Article
Language:English
Subjects:
Computation
Exact sciences and technology
Formalism
Hermite polynomials
Hermite–Sheffer polynomials
Mathematical analysis
Mathematical models
Mathematics
Monomiality principle
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Sheffer polynomials
Special functions
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Summary:In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite–Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite–Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite–Sheffer family.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.07.016