Second structure relation for \(q\)-semiclassical polynomials of the Hahn Tableau. (English) Zbl 1113.33022

Costas-Santos, R. S.; Marcellán, F.

J. Math. Anal. Appl. 329, No. 1, 206-228 (2007).

Only the first structure theorem for the \(q\)-semiclassical orthogonal polynomials exists. The authors propose a second structure relation. In doing so, the interplay of a general finite-type relation between a \(q\)-classical polynomial and the sequence of its \(q\)-differences is exploited.

Reviewer: Ravi N. Kalia (St. Cloud)

MSC:

33D99

Basic hypergeometric functions

Keywords:

q-classical orthogonal polynomials; q-Hahn Tableau

References:

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