The Askey-Wilson function transform scheme

Details The Askey-Wilson function transform scheme The Askey-Wilson function transform scheme

1999-12-17

arxiv.org/abs/math/9912140v2

Mathematics

Classical Analysis and ODEs

17 pages, 2 figures, AMS-TeX Some formulas corrected, reference updated

Scientific paper

In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function, and are Askey-Wilson functions, big q-Jacobi functions and little q-Jacobi functions and the corrresponding q-Bessel functions. The generalised orthogonality relations and the second order q-difference equations for these families are given. Limit transitions between these families are discussed. The quantum group theoretic interpretations are discussed shortly.

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