Материалы конференции. Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского
In this paper, we consider a linear homogeneous difference equation of the 2nd order with smooth coefficients. It is known that there are the several solutions to such equation. We have constructed explicit restrictions on the smoothness and growth of the coefficients of the equation, under which the solution retains the WKB form in an unbounded domain that does not contain pivot points and singularity points. The asymptotics of Laguerre polynomials are constructed for simultaneously large values of the argument and the order of the polynomials using proven asymptotic estimates as an application example.