Multiple orthogonal polynomials
Journal of Computational and Applied Mathematics
Some classical multiple orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Some discrete d-orthogonal polynomial sets
Journal of Computational and Applied Mathematics
Multiple Wilson and Jacobi-Piñeiro polynomials
Journal of Approximation Theory
Gaussian quadrature for multiple orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Multiple little q-Jacobi polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
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
d-orthogonality via generating functions
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Image analysis by discrete orthogonal dual Hahn moments
Pattern Recognition Letters
Difference equations for discrete classical multiple orthogonal polynomials
Journal of Approximation Theory
On Askey-scheme and d-orthogonality, I: A characterization theorem
Journal of Computational and Applied Mathematics
On some properties of q-Hahn multiple orthogonal polynomials
Journal of Computational and Applied Mathematics
Multiple Wilson and Jacobi--Piòeiro polynomials
Journal of Approximation Theory
Multiple little q-Jacobi polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Gaussian quadrature for multiple orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
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
Series Jackson Networks and Noncrossing Probabilities
Mathematics of Operations Research
Full length article: Asymptotics for the ratio and the zeros of multiple Charlier polynomials
Journal of Approximation Theory
Full length article: Asymptotics for the ratio and the zeros of multiple Charlier polynomials
Journal of Approximation Theory
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In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r + 1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r = 2.