Hypergeometric Orthogonal Polynomials and Their q-Analogues - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hypergeometric Orthogonal Polynomials and Their q-Analogues write by Roelof Koekoek. This book was released on 2010-03-18. Hypergeometric Orthogonal Polynomials and Their q-Analogues available in PDF, EPUB and Kindle. 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]).
The Askey-scheme of Hypergeometric Orthogonal Polynomials and Its Q-analogue
The Askey-scheme of Hypergeometric Orthogonal Polynomials and Its Q-analogue - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Askey-scheme of Hypergeometric Orthogonal Polynomials and Its Q-analogue write by Roelof Koekoek. This book was released on 1998. The Askey-scheme of Hypergeometric Orthogonal Polynomials and Its Q-analogue available in PDF, EPUB and Kindle.
Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials
Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials write by Richard Askey. This book was released on 1985. Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials available in PDF, EPUB and Kindle. A very general set of orthogonal polynomials in one variable that extends the classical polynomials is a set we called the q-Racah polynomials. In an earlier paper we gave the orthogonality relation for these polynomials when the orthogonality is purely discrete. We now give the weight function in the general case and a number of other properties of these very interesting orthogonal polynomials.
The Askey Scheme for Hypergeometric Orthogonal Polynomials
The Askey Scheme for Hypergeometric Orthogonal Polynomials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Askey Scheme for Hypergeometric Orthogonal Polynomials write by Nico M. Temme. This book was released on 2000. The Askey Scheme for Hypergeometric Orthogonal Polynomials available in PDF, EPUB and Kindle.
$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions
$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions write by Douglas Bowman. This book was released on 2002. $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions available in PDF, EPUB and Kindle. The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future
