Multiple little q-Jacobi polynomials

  • Authors:

  • Kelly Postelmans;Walter Van Assche

  • Affiliations:

  • Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium;Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
  • Year:
  • 2005

  • Generalizations of orthogonal polynomials

    Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad

  • Generalizations of orthogonal polynomials

    Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad

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Abstract

We introduce two kinds of multiple little q-Jacobi polynomials pn→ with multi-index nrarr; = (n1, n2 ..., nr) and degree |n→|= n1 + n2 + ... + nr by imposing orthogonality conditions with respect to r discrete little q-Jacobi measures on the exponential lattice {qk, k = 0, 1, 2, 3, ...}, where 0 q q-Jacobi polynomials have useful q-difference properties, such as a Rodrigues formula (consisting of a product of r difference operators). Some properties of the zeros of these polynomials and some asymptotic properties will be given as well.