TWO ERROR BOUNDS OF THE ELLIPTIC ASYMPTOTICS FOR THE FIFTH PAINLEVÉ TRANSCENDENTS

Abstract

For the fifth Painlevé equation it is known that a general solution is represented asymptotically by an elliptic function in cheese-like strips near the point at infinity. We present an explicit asymptotic formula for the error term of this expression, which leads to the error bound as was conjectured. An analogous formula with its bound is obtained for the error term of the correction function associated with the Lagrangian.