Kruglov V. E.
Solution of a Linear Second-Order Differential Equation with Coefficients Analytic in the Vicinity of a Fuchsian Zero Point
Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1381-1393
We obtain a solution of a second-order differential equation with coefficients analytic near a Fuchsian zero point. This solution is expressed via the hypergeometric functions and the fractional-order hypergeometric functions introduced in this paper.
Ukr. Mat. Zh. - 2009. - 61, № 6. - pp. 777-794
We present an efficient algorithm for the construction of a fundamental system of solutions of a linear finite-order difference equation. We obtain expressions in which all elements of this system are expressed via one of its elements and find a particular solution of an inhomogeneous equation.
Solution of a second-order Poincaré-Perron-type equation and differential equations that can be reduced to it
Ukr. Mat. Zh. - 2008. - 60, № 7. - pp. 900–917
The analytical solution of the second-order difference Poincare–Perron equation is presented. This enables us to construct in the explicit form a solution of the differential equation $$t^2(A_1t^2 + B_1t + C_1)u'' + t(A_2t^2 + B_2t + C_2)u' + (A_3t^2 + B_3t + C_3)u = 0 $$ The solution of the equation is represented in terms of two hypergeometric functions and one new special function. As a separate case, the explicit solution of the Heun equation is obtained, and polynomial solutions of this equation are found.
Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1473–1478
By using the methods of the theory of algebraic functions, we present an explicit construction of the canonical factorization of matrices of permutation type given on an open contour.
Ukr. Mat. Zh. - 1984. - 36, № 2. - pp. 247 - 252
The number of linearly independent functions which are multiples of a given divisor, and the vanishing of Riemann Θ-function
Ukr. Mat. Zh. - 1975. - 27, № 1. - pp. 101–107
Analog of the Cauchy kernel and the Riemann boundary problem of a three-sheeted surface of genus two
Ukr. Mat. Zh. - 1972. - 24, № 3. - pp. 351—366