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

Published online by Cambridge University Press:  20 November 2018

H. T. Koelink
H. T. Koelink*
Affiliation:
Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan200 B B-3001 Leuven (Heverlee) Belgium e–mail: erik.koelink@wis.KULeuven.ac.be
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Abstract

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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.

Keywords

33D8033D4533C4542C05addition formulaproduct formulabig q-Legendre polynomialslittle q-Jacobi polynomialsAl-Salam-Carlitz polynomialsquantum groupsSU(2)g-Charlier polynomialsLegendre polynomials.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 436 - 448
Copyright
Copyright © Canadian Mathematical Society 1995

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