Hypergeometric Orthogonal Polynomials and Their q-Analogues PDF
by Roelof Koekoek, Peter A. Lesky, Rene F. Swarttouw
Part of the Springer Monographs in Mathematics series
Description
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]).
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Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:18/03/2010
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- ISBN:9783642050145
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Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:18/03/2010
- Category:
- ISBN:9783642050145
