- #1

karlzr

- 131

- 2

## Homework Statement

A function F(a) is defined by [tex]F(a)=-ie^{-i\pi a/2}\int_{\pi/2-i\infty}^{\pi/2+i\infty}e^{ia(e^{iz}+z)}dz[/tex]

where the integration is along the vertical line ([itex]Re(z)=\pi/2[/itex]).

(a) Show that the integral is convergent for real and positive values of a.

(b) Find the saddle point(s) of the exponent.

(c) Find the path of steepest descent.

**2. The attempt at a solution**

I can handle the first two questions. However, I don't quite understand the last one. How to find the descent along a particular path? What does the last question ask about exactly?