Prove that

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- January 13th 2013, 11:05 PMsbhatnagarAn Interesting Integral
Prove that

- January 16th 2013, 09:53 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

- January 18th 2013, 02:40 AMzaidalyafeyRe: An Interesting Integral
How would you prove the convergence of this integral ... ?

- January 18th 2013, 12:33 PMSworDRe: An Interesting Integral
- January 19th 2013, 04:20 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