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Some expansions of functions based upon two sequences of hypergeometric polynomials. (English) Zbl 1461.30010

Summary: In this paper, we introduce two series expansions whose basis functions are two sequences of hypergeometric polynomials. We then present a systematic and detailed study of the general properties of each of these series expansions. We consider several illustrative examples to show the computational efficiency of our expansions in comparison to the usual Taylor series expansion. We also discuss some expansions of mixed types which are related to the results and assertions presented in this paper.

MSC:

30B10 Power series (including lacunary series) in one complex variable
30B50 Dirichlet series, exponential series and other series in one complex variable
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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