3 citations · 11 across the 5 of their papers we have counts for
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Preud's equations for orthogonal polynomials as discrete Painlevé equations
Alphonse P. Magnus
We consider orthogonal polynomials p_n with respect to an exponential weight function w(x) = exp(-P(x)). The related equations for the recurrence coefficients have been explored by…
Special non uniform lattice () orthogonal polynomials on discrete dense sets of points.
Alphonse P. Magnus
Difference calculus compatible with polynomials (i.e., such that the divided difference operator of first order applied to any polynomial must yield a polynomial of lower degree) c…
Painlevé equations for semi-classical recurrence coefficients
Alphonse P. Magnus
The title says it all.
Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equations: numerical explorations.
Alphonse P. Magnus
Generalized Jacobi polynomials are orthogonal polynomials related to a weight function which is smooth and positive on the whole interval of orthogonality up to a finite number of…
Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials.
Alphonse P. Magnus
Recurrence coefficients of semi-classical orthogonal polynomials (orthogonal polynomials related to a weight function such that is a rational function) are shown to be s…