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math.CA2021
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…
nlin.SI2021★ 6 cited
Different Hamiltonians for differential Painlevé equations and their identification using a geometric approach
Anton Dzhamay, Galina Filipuk, Adam Ligȩza +1
It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique -- there are many v…