We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation 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 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.
CITATION STYLE
Koekoek, R., Lesky, P., & Swarttouw, R. (2010). Hypergeometric orthogonal polynomials and their q-analogues. Journal of Mathematical Analysis and Applications (Vol. 389, pp. 108–118). Retrieved from http://books.google.com/books?hl=en&lr=&id=2TI8izIniZQC&oi=fnd&pg=PR5&dq=Hypergeometric+Orthogonal+Polynomials+and+Their+q-Analogues&ots=gTh_TuBZfe&sig=fufAxZl-QRWPfuDvHWxHCi9qD3A
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