We consider configurations of arbitrary scatterers (s= 1, … ,N) in two dimensions, such that the circles circumscribing the scatterers do not intersect. As shown previously [V. Twersky, inElectromagnetic Waves, R. E. Langer, Ed. (University of Wisconsin Press, Madison, 1962), pp. 361–389], the solution can be written in terms of the multiple‐scattered scattering amplitudesGs, and theGsare specified by the presumably known farfield isolated scattering amplitudesgsby a set of integral equationsG(g) (which can be converted to algebraic equations involving Hankel functions of the separationsbst, etc.). Among other applications, the previous paper gave the complete asymptotic series forG(g) in inverse powers of theb's; this was based essentially on Hankel's asymptotic expansion for the Hankel functionsHn. The present paper derives the analogous convergent representation ofG(g) based on the exact representation ofHnin terms of Lommel polynomials. ForNscatterers, we give the multiple‐scattering solution as a series inH0,H1,b−n, and the derivatives ofgwith respect to angles. For two scatterers, we give a closed form in terms of a differential operator.