Transformations of the measure of orthogonality for orthogonal polynomials, namely Freud transformations, are considered. Jacobi matrix of the recurrence coefficients of orthogonal polynomials possesses an isospectral deformation under these transformations. Dynamics of the coefficients are describe
Bell polynomials and differential equations of Freud-type polynomials
β Scribed by A. Bernardini; P.E. Ricci
- Book ID
- 104351131
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 278 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0895-7177
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β¦ Synopsis
By
using elementary properties of the Bell polynomials, and the classical factorization method, we derive in a simple way the differential equations satisfied by a class of Freud-type polynomials
π SIMILAR VOLUMES
Assume that {P~(x)}~0 are orthogonal polynomials relative to a quasi-definite moment functional a, which satisfy a differential equation of spectral type of order D (2 ~\\_-0, and k = 0.
In 1929, S. Bochner identified the families of polynomials which are eigenfunctions of a second-order linear differential operator. What is the appropriate generalization of this result to bivariate polynomials? One approach, due to Krall and Sheffer in 1967 and pursued by others, is to determine wh