Restortion of function on its moments in transfer theory

The method for reconstructing a function on the basis of its moment, developed by Spencer in the theory of penetration of fast electrons into matter, is modified in the present paper in such a manner as to eliminate the arbitrariness in selecting the parameters of the approximating function, as well as in constructing the sought distribution. In the modified method the parameters of the approximating function are determined solely by the moments of the sought distribution and by requiring satisfaction of recurrent relationships between the moments of the approximating function. The sought distribution is represented by two (for the odd and the even distributions) infinite series of approximating functions. The terms of these series contain parameters which are found from two corresponding systems of nonlinear equations by the method of successive a pproximations, which makes it, in principle, possible to obtain a solution with any desired accuracy. In positive direction of motion of the penetrating electrons the results of this paper are very close to those calculated by Spencer, whereas in the opposite direction they diverge perceptibly.