Mahola Y. Convexity, close-to-convexity and growth of entire solutions of linear differential equations with polynomial coefficients

In the thesis the n-member recurrent formula for Taylor's coefficients of the entire solution for linear differential equations of n-th order with polynomial coefficients is obtained. The conditions, under which the solutions of such equations with some sequence of its derivatives are convex or close-to-convex functions in the case when the n-member recurrent formula is reduced to a one-member or two-member recurrent formula are obtained. The growth of such functions is studied. The properties of entire solutions of the linear differential equations of the third order with polynomial coefficients are investigated.