Before trying to solve the problem I present here in this note, please make sure that you have read the complete note clearly.
Problem. Prove where and such that
Proof. Ofcoure, you can prove it in a several ways, like simplifying using complex analysis or using series expansion or maybe some other method(s).
But I'll share another elegant solution to the above problem.
Consider the following integral
We can also evaluate the above integral as
Now, here I have a problem. When I tried to verify the above result on Mathematica, it gives me the negative result. Here's a screenshot of my code (in particular, I did it for and for ). I expected Mathematica to return true for all values.
Can somebody help me, where am I going wrong. Is there a flaw in the result that I have proven , or is my Mathematica code wrong?