APPLICATION OF EXPANSIONS OF ENTIRE FUNCTIONS IN SERIES OF EXPONENTIALS

Abstract

The equality (1)is established for those values of for which the left-hand side is nonnegative. Here 1.$ SRC=http://ej.iop.org/images/0025-5734/54/1/A08/tex_sm_2965_img3.gif/>It is assumed that the () are the zeros of an entire function (), that and that the right-hand side of (1) is finite. It follows from this result that the indicator of is determined by the moduli of the coefficients .The equation (2)is also considered. Let and let be a convex function of . If ( is the indicator of for order ) then equation (2) has a solution with . It is shown by using the results stated above that there are not always solutions of (2) satisfying the condition .Bibliography: 8 titles.