THE FOURTH PAINLEVE EQUATION AND ASSOCIATED SPECIAL POLYNOMIALS

In this article rational solutions and associated polynomials for the fourth Painleve equation are studied. These rations of the fourth Painleve equation are expressible as the logarithmic derivative of special polinomials, the Okamoto polynomials. The structure of the roots of these Okamoto polynomials is studied and it is shown that these have a highly regular structure. The properties of the Okamoto polynomials are compared and contrasted with those of classical orthogonal polynomials.