On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point - Mokhonko, A. Z.; Mokhonko, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
Assume that the coefficients and solutions of the equation f^(n)+p_n−1(z)f^(n−1) +...+ p_s+1(z)f^(s+1) +...+ p_0(z)f = 0 have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients p_j , j = s+1, . . . ,n−1, increase slower (in terms of the Nevanlinna characteristics) than p_s(z). It is proved that this equation has at most s linearly independent solutions of finite order.