On Hadamard compositions of Gelfond–Leont'ev derivatives of analytic functions

For analytic functions $f$ and $g$ given by power series with different finite convergence radii, properties of the Hadamard composition of their Gelfond–Leont'ev derivatives is investigated. For study, generalized orders are used. The connection between the growth of the maximal term of the Hadamard composition of Gelfond–Leont'ev derivatives and the growth of the maximal term of the Gelfond–Leont'ev derivative of Hadamard composition is established. Similar results is obtained in terms of the classical order and lower order of growth.