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-difference operators for orthogonal polynomials

โœ Scribed by Mourad E.H. Ismail; Plamen Simeonov

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
763 KB
Volume
233
Category
Article
ISSN
0377-0427

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๐Ÿ“œ SIMILAR VOLUMES

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Differential and difference operators having orthogonal polynomials with two linear perturbations as eigenfunctions
โœ H. Bavinck ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 463 KB

In this paper we consider the polynomials {P~'V(x)}~0, orthogonal with respect to a certain symmetric bilinear form of Sobolev type. These polynomials are the result of two linear perturbations to the orthogonal polynomials {Pn(x)}~0, eigenfunctions of a linear differential or difference operator L.

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โœ M. Foupouagnigni; W. Koepf; A. Ronveaux ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 237 KB

We derive the fourth-order difference equation satisfied by the associated order r of classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials a and z which appear in the discrete Pearson equation A(ap)= zp defining the weight