Browsing by Author "Sous la direction de : Prof Walter Van Assche"

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    Orthogonal polynomials and Painleve equations : Deformed Laguerre weight function and Painleve equation V (PV).
    (UB, FS, 2022) Kubwimana, Gervais; Sous la direction de : Prof Walter Van Assche
    In this work, we focus on the link between orthogonal polynomials and Painlev e equations. We investigate the orthogonal polynomials with respect to the deformed Laguerre weight function w(x; t) = x (x + 1) e􀀀tx; x 2 [0;1[; > 􀀀1; 2 R; t > 0. By applying the Ladder operators approach to our weight function, we show that the recurrence coe cients of monic polynomial with respect to this weight are in terms of auxiliary quantities Rn(t) and rn(t) that satisfy the coupled Ricatti equations from which we nd that Rn(t), up to a certain linear fractional transformation, satis es a particular fth Painlev e equation PV ( 2 2 ;􀀀 2 2 ; 2n + 1 + + ;􀀀1 2 ). This is the main contribution of our work and is contained in the Theorem 3.6.