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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.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type 41A10 Approximation by polynomials 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
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##### References:
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