| Abstract: | On the basis of the connection between the theories of linear and nonlinear special functions, we present a method which makes it possible to consider the well known formal limits from complicated Painlevé equations to simpler ones as the double asymptotics of specific solutions of these equations with respect to the parameter and the argument under some special relation between them. The hierarchies of the first and second Painlevé equations are interpreted as special functions that describe the isomonodromic collision of turning points for linear systems of ordinary differential equations. Bibliography: 28 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 187, pp. 53–74, 1990. Translated by B. M. Bekker. |
