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2 results

  • Associated Continuous Hahn Polynomials

  • Dharma P. Gupta, Mourad E. H. Ismail, David R. Masson
  • Journal:
    Canadian Journal of Mathematics / Volume 43 / Issue 6 / 01 December 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 1263-1280
    Print publication:
    01 December 1991
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  • Explicit solutions to the recurrence relation for associated continuous Hahn polynomials are derived using 3F2 contiguous relations. These solutions are used to obtain a new continued fraction and the associated absolutely continuous measure. An exceptional case is shown to yield entry 33 in Chapter 12 of Ramanujan's second notebook.

  • Two Families of Associated Wilson Polynomials

  • M. E. H. Ismail, J. Letessier, G. Valent, J. Wimp
  • Journal:
    Canadian Journal of Mathematics / Volume 42 / Issue 4 / 01 August 1990
    Published online by Cambridge University Press:
    20 November 2018, pp. 659-695
    Print publication:
    01 August 1990
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  • Two families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the polynomials and to compute the corresponding continued fractions. The absolutely continuous components of the orthogonality measures of both families are computed. Generating functions are also given.