Hypergeometric Orthogonal Polynomials and Their q-Analogues - Couverture rigide

Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F.

Couverture rigide

ISBN 10 : 3642050131 ISBN 13 : 9783642050138

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2010

Synopsis

The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969-1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 3642050131
• ISBN 13: 9783642050138
• Reliure: Relié
• Nombre de pages: 597
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Allemagne