[en] The direct operational method is used to transform the collision integral in the transport equation to a polynomial in derivatives with respect to lethargy. This polynomial is approximated by the Pade approximation technique. Different orders of Pade approximation give the well-known synthetic kernel. This procedure reduces the integro-differential form of the transport equation to differential form. It also gives us the possibility to consider energy dependent cross-section and to get the solution without using the integral transform method. We shall consider here the solution for infinite homogeneous medium and calculate the energy deposition factor for different orders of the Pade approximant. (author)