Two error bounds of the elliptic asymptotics for the fifth Painlevé transcendents

Shun Shimomura

Published 2023-07-04Version 1

For the fifth Painlev\'e 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 an estimate for its magnitude as was conjectured. Analogous formula is obtained for the error term of the correction function associated with the Lagrangian.