On Analytical Solution of Ambartsumian Equation

Abstract

The Ambartsumian equation is used in the theory of surface brightness in milky way. This equation is a linear differential equation involving a proportional delay term. In this paper we use the Daftardar-Gejji and Jafari method to obtain analytical solution of Ambartsumian equation. The solution is provided in the form of a power series which is convergent for all reals. We prove the convergence of this series and plot solution graphs.