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A simple proof of Koornwinder’s addition formula for the little $q$-Legendre polynomials

Author: Mizan Rahman
Journal: Proc. Amer. Math. Soc. 107 (1989), 373-381
MSC: Primary 33D45; Secondary 33D80
MathSciNet review: 979214
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Abstract: Recently Koornwinder found an addition formula for the little $q$-Legendre polynomials by using Masuda et al.’s result that they are related to the matrix elements of the irreducible unitary representation of the twisted ${\text {SU(2)}}$ quantum group. Here we give an alternate derivation of the addition formula by using some summation and transformation formulas of basic hypergeometric series.

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Article copyright: © Copyright 1989 American Mathematical Society