Doubt on phase stationary method

[Asteroid]

Can the phase stationary method be applied to complex functions? And if it does, is it still called phase stationary method? I ask this because there are several methods for asymptotic analysis and I need to be sure if I can use this method for complex function. Is there any difference with the steepest descent method? Thanks.

 

[Ssnow]

yes, the steepest descent method is essentially the stationary method in the complex case ...

 

[Asteroid]

Another question, is there a reference on this to prove there are the same thing? Because I use this in my thesis and I need to be sure

 

[Ssnow]

No wait, sorry I intended was analogue not the same thing, in fact I think the steepest descent is more general ...

 

[Ssnow]

I suggest you to see the post of @blue_leaf77 of Feb 16, 2015, if you want the link:

https://www.physicsforums.com/threads/steepest-descent-vs-stationary-phase-method.798186/