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Connection problems via lowering operators. (English) Zbl 1061.33006
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.

33C45Orthogonal polynomials and functions of hypergeometric type
41A10Approximation by polynomials
41A58Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Full Text: DOI
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