Classical Orthogonal Polynomials as Moments
Copyright policy )Classical Orthogonal Polynomials as Moments
AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.
- University of Minnesota Morris United States
- University of Minnesota United States
- University of Minnesota System United States
- State University System of Florida United States
- Florida Southern College United States
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Generalized basic hypergeometric series, Al-Salam-Chihara polynomials, multilinear generating functions, Moment problems and interpolation problems in the complex plane
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Generalized basic hypergeometric series, Al-Salam-Chihara polynomials, multilinear generating functions, Moment problems and interpolation problems in the complex plane
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