The paper deals with the usual asymptotic expansion of the - function,
Based on the recent work of M. V. Berry and C. J. Howls [Proc. R. Soc., Lond., Ser. A 434, No. 1892, 657-675 (1991; Zbl 0764.30031)] the author derives integral formulas for the coefficients and the remainder term . As a result he obtains explicit and good bounds for the remainder terms of the Stokes line , the transition formula connecting the different asymptotic relations and the asymptotic behaviour of the coefficients as .