In terms of generalized orders the growth of this composition and their derivatives is investigated. A relation between the behavior of the maximal terms of the Hadamard composition of the derivatives and of the derivative of the Hadamard composition is established.
Let F and G be analytic functions given by Dirichlet series with exponents increasing to +
∞ and zero abscissa of absolute convergence.The growth of F with respect to G is studied through the generalized order. Formulas are found for the finding these quantities.
