find in the limit [tex]r\rightarrow\infty[/tex]
the solution (or rather a hint) given by the book:
"The integrand, considered as a complex function of p, has brunch cuts on the imaginary axis starting at [tex]\pm im[/tex].
To evaluate the integral we push the contour up to wrap around the upper branch cut. Defining [tex]\rho = - ip[/tex], we obtain
in the limit, tends to
The Attempt at a Solution
I can't find any theorem in complex analysis that permits a "push" of the contour shown in the figure, so I try the contour shown below:
but when I take limit R goes to infinity, the maximum modulus integral bound around the semicircle doesn't go to zero. so I'm stuck. Expert pls help me.