34 citations · 281 across the 51 of their papers we have counts for
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Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice
Mourad E. H. Ismail, Erik Koelink, Pablo Román
A general family of matrix valued Hermite type orthogonal polynomials is introduced and studied in detail by deriving Pearson equations for the weight and matrix valued differentia…
Matrix valued Laguerre polynomials
Erik Koelink, Pablo Román
Matrix valued Laguerre polynomials are introduced via a matrix weight function involving several degrees of freedom using the matrix nature. Under suitable conditions on the parame…
corepresentations and bivariate -Krawtchouk polynomials
Geoffroy Bergeron, Erik Koelink, Luc Vinet
The matrix elements of unitary corepresentations, which are analogues of the symmetric powers of the natural repesentation, are shown to be the bivariate -Krawtchouk o…
q-special functions, basic hypergeometric series and operators
Erik Koelink
In the lecture notes we start off with an introduction to the -hypergeometric series, or basic hypergeometric series, and we derive some elementary summation and transformation…
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
Mourad E. H. Ismail, Erik Koelink, Pablo Román
Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its -analogue.…