praharmitra
- 308
- 1
I am doing some calculation and am now stuck with an integral of the form
[tex]\lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)}[/tex]
for some function [itex]f(t)[/itex]. I don't know what the exact form of [itex]f(t)[/itex] is.
Is there any way to address this integral? Similar to the saddle-point method perhaps? The saddle-point method does not work here right? since the argument of the exponential does not have a minima.
How should I go about this?
Can we say that this integral is dominated by a certain value of [itex]t[/itex], say at [itex]t=1[/itex]? Why or why not?
[tex]\lim_{r \to \infty} \int_{-1}^1 dt f(t) e^{i r (t-1)}[/tex]
for some function [itex]f(t)[/itex]. I don't know what the exact form of [itex]f(t)[/itex] is.
Is there any way to address this integral? Similar to the saddle-point method perhaps? The saddle-point method does not work here right? since the argument of the exponential does not have a minima.
How should I go about this?
Can we say that this integral is dominated by a certain value of [itex]t[/itex], say at [itex]t=1[/itex]? Why or why not?