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Multiple Meixner Polynomials on a Non-Uniform Lattice

Author

Listed:
  • Jorge Arvesú

    (Department of Mathematics, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911 Leganés, Madrid, Spain)

  • Andys M. Ramírez-Aberasturis

    (Department of Mathematics, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911 Leganés, Madrid, Spain)

Abstract

We consider two families of type II multiple orthogonal polynomials. Each family has orthogonality conditions with respect to a discrete vector measure. The r components of each vector measure are q -analogues of Meixner measures of the first and second kind, respectively. These polynomials have lowering and raising operators, which lead to the Rodrigues formula, difference equation of order r + 1 , and explicit expressions for the coefficients of recurrence relation of order r + 1 . Some limit relations are obtained.

Suggested Citation

  • Jorge Arvesú & Andys M. Ramírez-Aberasturis, 2020. "Multiple Meixner Polynomials on a Non-Uniform Lattice," Mathematics, MDPI, vol. 8(9), pages 1-33, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1460-:d:406783
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