84 citations · 737 across the 52 of their papers we have counts for
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Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
Jan F. van Diejen
Two families (type and type ) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and…
Multivariable q-Racah polynomials
Jan F. van Diejen, Jasper V. Stokman
The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measu…
Properties of some families of hypergeometric orthogonal polynomials in several variables
Jan F. van Diejen
Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of…
Commuting difference operators with applications to orthogonal polynomials in several variables
J. F. van Diejen
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence rel…
Self-dual Koornwinder-Macdonald polynomials
Jan F. van Diejen
We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used t…
On the diagonalization of difference Calogero-Sutherland systems
Jan F. van Diejen
We discuss the simultaneous diagonalization of a family of commuting difference operators by Koornwinder's multivariable generalization of the Askey-Wilson polynomials. The operato…