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Linearization and connection coefficients for hypergeometric-type polynomials. (English) Zbl 0927.33005
By use of the coefficients of the second-order linear differential equation defining orthogonal polynomials of hypergeometric type the authors derive explicite formulas as well for the coefficients of the linearization of a product of two hypergeometrie polynomials in terms of an orthogonal set of hypergeometrie polynomials as the connection coefficients which appear if the degree of one factor of the product equals zero. The method is applicated to Jacobi, Laguerre, Hermite and Bessel polynomials.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
26C05 Real polynomials: analytic properties, etc.
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