Abstract
We advocate the exploitation of symmetry (recurrence relation) techniques for the derivation of properties associated with families of basic hypergeometric functions, in analogy with the local Lie theory techniques for ordinary hypergeometric functions. Here these ideas are motivated from the theory of partial differential equations and then applied to the (continuous) Askey-Wilson polynomials, q-Hahn and big and little q-Jacobi polynomials to obtain strikingly simple derivations (rather than verifications) of their orthogonality relations and associated integrals. Some q-analogs of Barnes’ First Lemma are also derived as examples. This expository paper is based on joint work with Ernie Kalnins. Similar methods have been used by Nikiforov, Suslov and Uvarov.
Work supported in part by the National Science Foundation under grant DMS 86-00372
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Miller, W. (1989). Symmetry Techniques and Orthogonality for q-Series. In: Stanton, D. (eds) q-Series and Partitions. The IMA Volumes in Mathematics and Its Applications, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0637-5_15
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DOI: https://doi.org/10.1007/978-1-4684-0637-5_15
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