## The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue (1998)

Citations: | 409 - 6 self |

### BibTeX

@MISC{Koekoek98theaskey-scheme,

author = {Roelof Koekoek and René F. Swarttouw},

title = {The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue},

year = {1998}

}

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### Abstract

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials and we give a q- analogue 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 di#erential or di#erence 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 di#erent 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 di#erence 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...