Multiple orthogonal polynomials associated with macdonald functions
By Walter Van Assche, S. Yakubovich. 2000
68 citations recorded by the source corpus.
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bassel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Padé table. We give some properties of these polynomials: differential properties, a Rodrigues type formula and explicit formulas for the third order linear recurrence relation.
Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e02e16fedcaece4ca26fb5ac03b7bf7226f9f81f
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In Atomic and Molecular Physics, and Optics
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- On the classical {$d$}-orthogonal polynomials defined by certain generating functions. II (2000, methodology): “These polynomials have been studied recently by the authors [6] and by Van Assche and Yakubovich [36] in order to solve an open problem, formulated by Prudnikov in [35], which consists of constructing orthogonal polynomials associated with the weight function ρν(x) = 2x ν 2Kν(2 √ x), x > 0, where Kν”
- Some discrete d -orthogonal polynomial sets (2003, background): “The continuous case was studied, for instance, in [3,4,14,25,26].”