The singular points of series of exponents on the boundary of convergence domain

We study singular points of series of exponents. The result which is special cases of results of G. Hadamard, E. Fabry, V. Bernstein, G. Polya, is obtained. At that we construct the special function, it has not singular points on a boundary of convergence domain of it's own series. This function is the generalization of special function from the theory of Dirichlet's series on a case of general series of exponents.