I have a question about an application of the residue theorem to real definite integrals.
In "COMPLEX ANALYSIS" by Ahlfors, there is the following statement:
The integral
where P(z) and Q(z) are polynomials of degree m and n, respectively,
exists if and only if
and Q(z) has no zeros on real axis.
A brief proof of the sufficiency follows the statement.
But, there isn't the proof of the necessity.
And, I couldn't find it in any other book on complex analysis.
I'm grateful if someone could give me a proof of the necessity of the statement above.