On a Pollaczek-Jacobi type orthogonal polynomials

We study a sequence of polynomials orthogonal with respect to a family weights w(x) := w(x, t) = e x(1− x) , t ≥ 0, over [−1, 1]. If t = 0, this reduces to a shifted Jacobi weight. Our ladder operator formalism and the associated compatibility conditions give an easy determination of the recurrence coefficients. For t > 0, the deformation term e−t/x induces an infinitely strong zero at x = 0. The resulting t dependence of the recurrence coefficients is expressed in terms of a set of auxiliary quantities. These are a particular Painlevé V and/or allied functions. It is shown that the logarithmic derivative of the Hankel determinant,