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1 results

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

  • H. T. Koelink
  • Journal:
    Canadian Journal of Mathematics / Volume 47 / Issue 2 / 01 April 1995
    Published online by Cambridge University Press:
    20 November 2018, pp. 436-448
    Print publication:
    01 April 1995
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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.