Show that (where is Euler's constant).
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Hint: Spoiler: Start with the fact that
Bigger Hint: Spoiler:
Last edited by Random Variable; Jan 24th 2011 at 10:41 AM.
Originally Posted by Random Variable Show that (where is Euler's constant). I would proceed as follows: Spoiler:
Let . By previous problem we have that for and thus on that interval
That said, using Lebniz's differentiation under the integral technique (checking that it's applicable) we find that
Thus, our integral is .
It's amazing how I don't realize that many of the problems I post are interconnected until you point it out to me.
Originally Posted by Random Variable It's amazing how I don't realize that many of the problems I post are interconnected until you point it out to me.
Yeah, but I'm often lazy and just look for the quickest most mechanical solution, you take time and come up with neat non-obvious solutions. So, in the end, which is better?
Can we justify changing the order of integration, or is my solution invalid?
Last edited by uniquesailor; Feb 16th 2011 at 01:19 PM.
Originally Posted by uniquesailor ... What is 'MAZ identity', if you don't mind me asking?
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