The renormalizing series of some integral equations

We consider integral equations for which the perturbation expansion gives a power series in a parameter $h$ whose coefficients are divergent integrals. We eliminate the divergent integrals by introducing a renormalizing $Z(t,h)$ series in the minimal subtraction scheme. We investigate the convergence of the formal $Z$ series in relation to the kernels of the integral equations. We find a relation of the renormalizing series to the Lagrange inversion series and also some other relations.