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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
Mourad E. H. Ismaila, Erik Koelinkb, Pablo Románc a University of Central Florida, Orlando, Florida 32816, USA
b IMAPP, Radboud Universiteit, PO Box 9010, 6500GL Nijmegen, The Netherlands
c CIEM, FaMAF, Universidad Nacional de Córdoba, Medina Allende s/n Ciudad Universitaria, Córdoba, Argentina
Аннотация:
Burchnall's method to invert the Feldheim–Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue. The resulting expansion formulas are made explicit for several families corresponding to measures with infinite support, including the Wilson and Askey–Wilson polynomials. An integrated version gives the possibility to give alternate expression for orthogonal polynomials with respect to a modified weight. This gives expansions for polynomials, such as Hermite, Laguerre, Meixner, Charlier, Meixner–Pollaczek and big $q$-Jacobi polynomials and big $q$-Laguerre polynomials. We show that one can find expansions for the orthogonal polynomials corresponding to the Toda-modification of the weight for the classical polynomials that correspond to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre, Charlier, Meixner, Meixner–Pollaczek and Krawtchouk polynomials.
Ключевые слова:
orthogonal polynomials; Askey scheme and its $q$-analogue; expansion formulas; Toda lattice.
Поступила: 27 февраля 2018 г.; в окончательном варианте 11 июля 2018 г.; опубликована 17 июля 2018 г.
Образец цитирования:
Mourad E. H. Ismail, Erik Koelink, Pablo Román, “Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions”, SIGMA, 14 (2018), 072, 24 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1371 https://www.mathnet.ru/rus/sigma/v14/p72
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