56 citations · 289 across the 35 of their papers we have counts for
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Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation
Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar +1
We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities invol…
On classical orthogonal polynomials on bi-lattices
K. Castillo, G. Filipuk, D. Mbouna
In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomi…
Differential equations for the recurrence coefficients of semi-classical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
Anton Dzhamay, Galina Filipuk, Alexander Stokes
In this paper we present a general scheme for how to relate differential equations for the recurrence coefficients of semi-classical orthogonal polynomials to the Painlevé equation…
Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities
Thomas Kecker, Galina Filipuk
In a 1979 paper, K. Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initia…
Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials
Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators and and, as…
On the derivatives of the Heun functions
G. Filipuk, A. Ishkhanyan, J. Dereziński
The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions…