Difference equations for discrete classical multiple orthogonal polynomials

  • Authors:

  • D. W. Lee

  • Affiliations:

  • Department of Mathematics, Teachers College, Kyungpook National University, Taegu 702-701, Republic of Korea

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2008

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Abstract

For discrete multiple orthogonal polynomials such as the multiple Charlier polynomials, the multiple Meixner polynomials, and the multiple Hahn polynomials, we first find a lowering operator and then give a (r+1)th order difference equation by combining the lowering operator with the raising operator. As a corollary, explicit third order difference equations for discrete multiple orthogonal polynomials are given, which was already proved by Van Assche for the multiple Charlier polynomials and the multiple Meixner polynomials.