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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
DOI: https://doi.org/10.1090/S0002-9939-1989-0979214-3
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.


References [Enhancements On Off] (What's this?)

  • [1] G. E. Andrews and R. Askey, Enumeration of partitions: The role of Eulerian series and $ q$orthogonal polynomials, pp. 3-26 in Higher Combinatorics, ed. M. Aigner, Reidel, 1977. MR 519776 (80b:10021)
  • [2] T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, 1978. MR 0481884 (58:1979)
  • [3] G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge University Press, (to appear). MR 2128719 (2006d:33028)
  • [4] T. H. Koornwinder, The addition formula for little $ q$-Legendre polynomials and the twisted $ {\text{SU(2)}}$ quantum group, (to appear).
  • [5] T. Masuda, K. Minachi, V. Nakagami, M. Noumi, and K. Ueno, Representations of quantum groups and a $ q$-analogue of orthogonal polynomials, C. R. Acad. Sci. Paris, Sér. I Math. 307 (1988), 559-564. MR 967361 (90a:17013)
  • [6] S. L. Woronowicz, Compact matrixpseudogroups, Comm. Math. Phys. 111 (1987), 613-665. MR 901157 (88m:46079)
  • [7] -, Twisted $ {\text{SU(2)}}$ group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), 117-181. MR 890482 (88h:46130)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0979214-3
Article copyright: © Copyright 1989 American Mathematical Society

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