Abstract
In this chapter we deal with all families of basic hypergeometric orthogonal polynomials appearing in the q-analogue of the Askey scheme on the page 413. For each family of orthogonal polynomials we state the most important properties such as a representation as a basic hypergeometric function, orthogonality relation(s), the three-term recurrence relation, the second-order q-difference equation, the forward shift (or degree lowering) and backward shift (or degree raising) operator, a Rodrigues-type formula and some generating functions. Throughout this chapter we assume that 0<q<1. In each case we use the notation which seems to be most common in the literature. Moreover, in each case we also state the limit relations between various families of q-orthogonal polynomials and the limit relations (q→1) to the classical hypergeometric orthogonal polynomials belonging to the Askey scheme on page 183. For notations the reader is referred to chapter 1.
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© 2010 Springer-Verlag Berlin Heidelberg
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Koekoek, R., Lesky, P.A., Swarttouw, R.F. (2010). Basic Hypergeometric Orthogonal Polynomials. In: Hypergeometric Orthogonal Polynomials and Their q-Analogues. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05014-5_14
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DOI: https://doi.org/10.1007/978-3-642-05014-5_14
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05013-8
Online ISBN: 978-3-642-05014-5
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