Riley hobson bence · Problem 25.23

Tensors

Mathematics — Methods · steepest-descents-asymptotic-approximation

Problem

Use the method of steepest descents to find an asymptotic approximation, valid for

z

large, real and positive, to the function defined by

F_\nu(z) = \int_C \exp(-iz\sin t + i\nu t)\, dt,

where

\nu

is real and non-negative and

C

is a contour that starts at

t = -\pi + i\infty

and ends at

t = -i\infty