Connection problems and matrix representations for certain hybrid polynomials. (English) Zbl 1435.33025

Summary: In this paper, we deal with the connection and duplication problems associated with the hybrid Sheffer family. The hybrid Sheffer polynomials are also studied via matrix approach. The properties of these polynomials are established using simple matrix operations. Examples providing the corresponding results for certain members of the hybrid Sheffer family are considered. This article is first attempt in the direction of obtaining connection and duplication coefficients and matrix representations for the hybrid polynomials.


33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
11B83 Special sequences and polynomials
15A16 Matrix exponential and similar functions of matrices
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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