PLEASE ATTEMPT TO SOLVE IT! If you are not 100 % sure that's okay, as long as you know how to solve some part of it. I promise will like your comment and will tell my friend to like it too. Thanks in advance!

PLEASE ATTEMPT TO SOLVE IT! If you are not 100 % sure that's okay, as long as you know how to solve some parts of a, b and c. Promise will like your comment and will tell my friend to like it too. Thanks in advance.

Problem 3 Consider a complex function, f(x), that is analytic on the upper half of the complex plane and goes to 0 as [2 00. (a) If the imaginary part of f(x) = v(x) = -1/(x2 + 1), use the dispersion relations and a principal part integral to find the real part of f(x), u(x). (b) What is f(x)? (c) Show that Lo dx u(x)/2 = L* dx \u(x)2 by direct evaluation of each integral. This is known as the Parseval Relation. Problem 3 Consider a complex function, f(x), that is analytic on the upper half of the complex plane and goes to 0 as [2 00. (a) If the imaginary part of f(x) = v(x) = -1/(x2 + 1), use the dispersion relations and a principal part integral to find the real part of f(x), u(x). (b) What is f(x)? (c) Show that Lo dx u(x)/2 = L* dx \u(x)2 by direct evaluation of each integral. This is known as the Parseval Relation