31 citations · 49 across the 7 of their papers we have counts for
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On the recurrence coefficients of generalized little -Laguerre polynomials
Galina Filipuk, Christophe Smet
In this paper we consider a semi-classical variation of the weight related to the little -Laguerre polynomials and obtain a second order second degree discrete equation for the…
The generalized Krawtchouk polynomials and the fifth Painlevé equation
Lies Boelen, Galina Filipuk, Christophe Smet +2
We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for thes…
Orthogonal polynomials on a bi-lattice
Christophe Smet, Walter Van Assche
We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-β. We combine both lattices to obtain the bi-lattice N \c…
Irrationality proof of a -extension of using little -Jacobi polynomials
Christophe Smet, Walter Van Assche
We show how one can use Hermite-Padé approximation and little -Jacobi polynomials to construct rational approximants for . These numbers are -analogues of the well kn…
-Discrete Painlevé equations for recurrence coefficients of modified -Freud orthogonal polynomials
Lies Boelen, Christophe Smet, Walter Van Assche
We present an asymmetric -Painlevé equation. We will derive this using -orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will o…
Irrationality proof of certain Lambert series using little q-Jacobi polynomials
Jonathan Coussement, Christophe Smet
We apply the Pade technique to find rational approximations to % \[h^{\pm}(q_1,q_2)=\sum_{k=1}^\infty\frac{\q_1^k}{1\pm \q_2^k}, 0<q_1,q_2<1, q_1\in\mathbb{Q}, q_2=1/p_2, p_2\in\ma…