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 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.
We would like to thank Professor Tom H. Koornwinder who suggested us to write a report like this. He also helped us solving many problems we encountered during the research and provided us with several references.