On integral representation to solutions for a differential equation with singular coefficients

We consider integral representations to solutions for a differential equation with singular coefficients with Bessel operator. An existence of such integral representations is proved by successive approximations using transmutation operators method. Unlike known results we consider potentials with strong singularities at the origin and also slightly improve well-known method of B. M. Levitan by more accurate calculation of Green function in terms of Legendre function. It leads to more precise estimates without unnecessary constants.