Addition Formula For Big q-Legendre Polynomials From The Quantum Su(2) Group

Koelink, H. T.

Canadian journal of mathematics, Tome 47 (1995) no. 2, pp. 436-448

Résumé

From Koornwinder's interpretation of big q-Legendre polynomials as spherical elements on the quantum SU(2) group an addition formula is derived for the big g-Legendre polynomial. The formula involves Al-Salam-Carlitz polynomials, little q-Jacobi polynomials and dual q-Krawtchouk polynomials. For the little q-ultraspherical polynomials a product formula in terms of a big q-Legendre polynomial follows by q-integration. The addition and product formula for the Legendre polynomials are obtained when q tends to 1.

Détail

DOI : 10.4153/CJM-1995-024-8

Mots-clés : 33D80, 33D45, 33C45, 42C05, addition formula, product formula, big q-Legendre polynomials, little q-Jacobi polynomials, Al-Salam-Carlitz polynomials, quantum groups, SU(2), g-Charlier polynomials, Legendre polynomials.

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