书目名称 | Hypergeometric Orthogonal Polynomials and Their q-Analogues |
编辑 | Roelof Koekoek,Peter A. Lesky,René F. Swarttouw |
视频video | http://file.papertrans.cn/431/430637/430637.mp4 |
概述 | Includes supplementary material: |
丛书名称 | Springer Monographs in Mathematics |
图书封面 |  |
描述 | 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 th |
出版日期 | Book 20101st edition |
关键词 | Askey scheme; Eigenvalue; Hypergeometric function; basic hypergeometric functions; differential equation |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-642-05014-5 |
isbn_softcover | 978-3-642-26351-4 |
isbn_ebook | 978-3-642-05014-5Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
issn_series | 1439-7382 |
copyright | Springer-Verlag Berlin Heidelberg 2010 |