Expansions of one density via polynomials orthogonal with respect to the other. (English) Zbl 1232.33019
The article exploits the fact that there is an infinite sum formula that expresses the density of one family of orthogonal polynomials in terms of another family provided that one knows the connection coefficients that allow to represent the first family in terms of the other family. In this way, the author discovers various new densities by given ones. Various examples supplement this result.
Reviewer: Carsten Schneider (Linz)
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
orthogonal polynomials; \(q\)-Hermite polynomials; Al-Salam-Chihara polynomials; Chebyshev polynomials; Rogers polynomials; connection coefficients; positive kernels; kernel expansion; Poisson-Mehler expansion; \(q\)-Gaussian distribution; Wigner distribution; Kesten-McKay distributionReferences:
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