Multiple Meixner Polynomials on a Non-Uniform Lattice

Jorge Arvesú and Andys M. Ramírez-Aberasturis
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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

Mathematics, 2020, vol. 8, issue 9, 1-33

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.

Keywords: Hermite–Padé approximation; multiple orthogonal polynomials; discrete orthogonality; recurrence relations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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