Hypergeometric orthogonal polynomials and their qanalogues
 Author/Creator
 Koekoek, Roelof, 1963
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2010.
 Physical description
 xix, 578 p. ; 25 cm.
 Series
 Springer monographs in mathematics.
Access
Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Definitions and Miscellaneous Formulas. Classical orthogonal polynomials. Orthogonal Polynomial Solutions of Differential Equations. Orthogonal Polynomial Solutions of Real Difference Equations. Orthogonal Polynomial Solutions of Complex Difference Equations. Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations. Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations. Hypergeometric Orthogonal Polynomials. Polynomial Solutions of Eigenvalue Problems. Classical qorthogonal polynomials. Orthogonal Polynomial Solutions of qDifference Equations. Orthogonal Polynomial Solutions in q?x of qDifference Equations. Orthogonal Polynomial Solutions in q?x+uqx of Real.
 (source: Nielsen Book Data)
 Publisher's Summary
 The present book is about the Askey scheme and the qAskey 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 19691970. 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]).
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2010
 Responsibility
 Roelof Koekoek, Peter A. Lesky, René F. Swarttouw ; with a foreword by Tom H. Koornwinder.
 Series
 Springer monographs in mathematics, 14397382
 ISBN
 9783642050138
 3642050131
 9783642050145
 364205014X