Prove that

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- Jan 14th 2013, 12:05 AMsbhatnagarAn Interesting Integral
Prove that

- Jan 16th 2013, 10:53 PMsbhatnagarRe: An Interesting Integral
This Problem is not as difficult as it looks. Use the property :

The first integral equals -1.

Let -------(1)

A property of definite integral says that

therefore

--------(2)

Add (1) and (2):

(from Euler's Reflection Formula! (Giggle))

Recall that .

Therefore

- Jan 18th 2013, 03:40 AMzaidalyafeyRe: An Interesting Integral
How would you prove the convergence of this integral ... ?

- Jan 18th 2013, 01:33 PMSworDRe: An Interesting Integral
- Jan 19th 2013, 05:20 PMSworDRe: An Interesting Integral
Here is another way to evaluate the integral. Write it out as a Riemann sum, the old-school way:

So

This exactly fits the format for the multiplication theorem for the gamma function! So