An explicit formula for the coefficients of the saddle point method (Q628669)

In continuation of a former paper [J. Math. Anal. Appl. 354, No. 1, 347--359 (2009; Zbl 1163.65013)] of the authors and \textit{E. P. Sinusía} there are given explicit formulae for the coefficients of the asymptotic expansion of the integral \[ \int_C \exp(-xf(z))g(z)\,dz \] over a path \(C\) in the complex plane as \(x\to\infty\) according to Watson's lemma, where \(f\) and \(g\) are analytic functions. The result is applied to Bessel's functions.