Hypergeometric orthogonal polynomials and their q-analogues
The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function. Replacing the differential...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2010. |
| Collection: | Springer Monographs in Mathematics
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| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Hypergeometric orthogonal polynomials and their q-analogues, Roelof Koekoek, Peter A. Lesky, René F. Swarttouw, Heidelberg, Springer, 2010, 1 vol. (XIX-578 p.), Springer monographs in mathematics, 978-3-642-05013-8 • Hypergeometric Orthogonal Polynomials and Their q-Analogues, Texte imprimé, 9783642050503 • Hypergeometric orthogonal polynomials and their q-analogues, Roelof Koekoek, Peter A. Lesky, René F. Swarttouw, Heidelberg, Springer, 2010, 1 vol. (XIX-578 p.), Springer monographs in mathematics, 978-3-642-05013-8 • Hypergeometric Orthogonal Polynomials and Their q-Analogues, Texte imprimé, 9783642263514 |
| Résumé: | The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function. Replacing the differential equation by a second-order difference equation results in (discrete) orthogonal polynomial solutions with similar properties. Generalizations of these difference equations, in terms of Hahn's q-difference operator, lead to both continuous and discrete orthogonal polynomials with similar properties. For instance, they can be expressed in terms of (basic) hypergeometric functions. Based on Favard's theorem, the authors first classify all families of orthogonal polynomials satisfying a second-order differential or difference equation with polynomial coefficients. Together with the concept of duality this leads to the families of hypergeometric orthogonal polynomials belonging to the Askey scheme. For each family they list the most important properties and they indicate the (limit) relations. Furthermore the authors classify all q-orthogonal polynomials satisfying a second-order q-difference equation based on Hahn's q-operator. Together with the concept of duality this leads to the families of basic hypergeometric orthogonal polynomials which can be arranged in a q-analogue of the Askey scheme. Again, for each family they list the most important properties, the (limit) relations between the various families and the limit relations (for q --> 1) to the classical hypergeometric orthogonal polynomials belonging to the Askey scheme. These (basic) hypergeometric orthogonal polynomials have several applications in various areas of mathematics and (quantum) physics such as approximation theory, asymptotics, birth and death processes, probability and statistics, coding theory and combinatorics |
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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783642050145 |
| ISSN: | 2196-9922 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |