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The Askey scheme of hypergeometric orthogonal polynomials and its q-analogue

✍ Scribed by Koekoek R., Swarttouw R.F.


Book ID
127398680
Year
2002
Tongue
English
Weight
686 KB
Edition
draft
Category
Library

No coin nor oath required. For personal study only.

✦ Synopsis


We list the so-called Askey-scheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differential or difference equation, the forward and backward shift operator, the Rodrigues-type formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between different classes of orthogonal polynomials listed in the Askey-scheme. In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation, second order difference equation, forward and backward shift operator, Rodrigues-type formula and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally, in chapter 5 we point out how the 'classical' hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.


πŸ“œ SIMILAR VOLUMES


A Set of Hypergeometric Orthogonal Polyn
✍ Askey, Richard; Wilson, James πŸ“‚ Article πŸ“… 1982 πŸ› Society for Industrial and Applied Mathematics 🌐 English βš– 433 KB