Difference equations for discrete classical multiple orthogonal polynomials

• Autores: D. W. Lee
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 150, Nº 2, 2008, págs. 132-152
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.06.002
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• Resumen

  • 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.