CONVERGENCE OF PRODUCT INTEGRATION RULES OVER (0, oo) FOR FUNCTIONS WITH WEAK SINGULARITIES AT THE ORIGIN

In this paper we consider integrals of the form / e-xK(x,y)f(x)dx, Jo with / 6 C[0, oo) n C«(0, oo), q > p > 0, and x¡f^'\x) 6 C[0, oo), / = I, ... , q -p , when q > p . They appear for instance in certain WienerHopf integral equations and are of interest if one wants to solve these by a Nyström method. To discretize the integral above, we propose to use a product rule of interpolatory type based on the zeros of Laguerre polynomials. For this rule we derive (weighted) uniform convergence estimates and present some numerical examples.