Hypergeometric Orthogonal Polynomials and Their q-Analogues

Hypergeometric Orthogonal Polynomials and Their q-Analogues by Roelof Koekoek
English | PDF | 2010 | 578 Pages | ISBN : 3642050131 | 5 MB
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.