Overview
- Authors:
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Roelof Koekoek
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Fac. Mathematics & Informatics, Delft University of Technology, Delft, Netherlands
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Peter A. Lesky
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Fakultät für Mathematik, Universität Stuttgart, Stuttgart, Germany
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René F. Swarttouw
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Dept. Mathematics &, Free University Amsterdam, Amsterdam, Netherlands
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Table of contents (14 chapters)
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 1-27
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 29-51
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 53-75
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Classical Orthogonal Polynomials
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Classical orthogonal polynomials
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 79-93
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 95-121
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 123-139
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 141-170
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 171-181
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 183-253
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Classical q-Orthogonal Polynomials
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Front Matter
Pages 255-255
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Classical q-orthogonal polynomials
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 257-322
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 323-367
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 369-394
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 395-411
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- Roelof Koekoek, Peter A. Lesky, René F. Swarttouw
Pages 413-552
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Back Matter
Pages 553-578
About this book
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]).
Reviews
From the reviews:
“The book starts with a brief but valuable foreword by Tom Koornwinder on the history of the classification problem for orthogonal polynomials. … the ideal text for a graduate course devoted to the classification, and it is a valuable reference, which everyone who works in orthogonal polynomials will want to own.” (Warren Johnson, The Mathematical Association of America, August, 2010)
Authors and Affiliations
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Fac. Mathematics & Informatics, Delft University of Technology, Delft, Netherlands
Roelof Koekoek
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Fakultät für Mathematik, Universität Stuttgart, Stuttgart, Germany
Peter A. Lesky
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Dept. Mathematics &, Free University Amsterdam, Amsterdam, Netherlands
René F. Swarttouw