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Zbl 1061.33006
Ben Cheikh, Y.; Chaggara, H.
Connection problems via lowering operators. (English)
[J] J. Comput. Appl. Math. 178, No. 1-2, 45-61 (2005). ISSN 0377-0427

Summary: The lowering operator $\sigma$ associated with a polynomial set $\{P_n\}_{n\geqslant 0}$ is an operator not depending on $n$ and satisfying the relation $\sigma(P_n)=nP_{n-1}$. In this paper, we express explicitly the connection coefficients between two polynomial sets using their corresponding lowering operators. We obtain some well-known results as particular cases including some duplication and addition formulas.

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type
41A10 Approximation by polynomials
41A58 Series expansions

Keywords: Connection coefficients; Lowering operators; s-Appell polynomials; Boas-Buck polynomials; Duplication formula; Addition formula

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Zentralblatt MATH Berlin [Germany]