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Документ Properties of solutions of a heterogeneous differential equation of the second order(2019) Mulyava, Oksana; Sheremeta, Miroslav; Trukhan, Yu. S.Suppose that a power seriesA(z) =∑∞n=0anznhas the radius of convergenceR[A]∈[1,+∞].For a heterogeneous differential equationz2w′′+ (β0z2+β1z)w′+ (γ0z2+γ1z+γ2)w=A(z)with complex parameters geometrical properties of its solutions (convexity, starlikeness and close-to-convexity) in the unit disk are investigated. Two cases are considered: ifγ26=0 andγ2=0. Wealso consider cases when parameters of the equation are realnumbers. Also we prove that for asolutionfof this equation the radius of convergenceR[f]equals toR[A]and the recurrent formulasfor the coefficients of the power series off(z)are found. For entire solutions it is proved that theorder of a solutionfis not less then the order ofA(̺[f]≥̺[A]) and the estimate is sharp. The sameinequality holds for generalized orders (̺αβ[f]≥̺αβ[A]). For entire solutions of this equation thebelonging to convergence classes is studied. Finally, we consider a linear differential equation of theendless order∞∑n=0ann!w(n)=Φ(z), and study a possible growth of its solutions.Документ On belonging of characteristic functions of probability laws to a convergence class(2013) Kulyavetc, Lubov; Mulyava, Oksana; Sheremeta, MiroslavIt is investigated the condition on a probability law, under which its characteristic function belongs to a convergence class. Досліджено умову на ймовірнісний закон відповідно до якого характеристична функція належить до класу збіжності.Документ Relation between the maximum modulus and the maximal term of Dirichlet series in terms of a convergence class(2012) Mulyava, Oksana; Sheremeta, Miroslav; Sumyk, O.A relation between the growth of maximum modulus and the growth maximal term of Dirichlet series in terms of a convergence class is investigated.Досліджено зв’язок між зростанням максимуму модуля і зростанням максимального члена ряду Діріхле в термінах класів збіжності.