WKB APPROXIMATION AND KRALL-TYPE ORTHOGONAL POLYNOMIALS

We give a unified approach to the Krall-type polynomials orthogonal wi th respect to a positive measure consisting of an absolutely continuou s one 'perturbed' by the addition of one or more Dirac delta functions . Some examples studied by different authors are considered from a uni que point of view. Also some properties of the Krall-type polynomials are studied. The three-term recurrence relation is calculated explicit ly, as well as some asymptotic formulas. With special emphasis will be considered the second order differential equations that such polynomi als satisfy. They allow us to obtain the central moments and the WKB a pproximation of the distribution of zeros. Some examples coming from q uadratic polynomial mappings and tridiagonal periodic matrices are als o studied.