The Askey-Wilson function transform scheme

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

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Classical Analysis and ODEs, Quantum Algebra, 33D15, 33D45 (Primary) 33D80 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/79625

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9912140
 http://arxiv.org/abs/math/9912140

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arXiv