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 Post subject: Calculus (15) Beta functionPosted: Sat, 20 Dec 2008 00:05:43 UTC
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Let where Suppose and are given such that Directly * evaluate

* You may only use the definition of and integration techniques!

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 Post subject: Posted: Sat, 20 Dec 2008 19:21:54 UTC
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Does that include cplx. analysis integration techniques?

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 Post subject: Posted: Fri, 26 Dec 2008 04:31:21 UTC
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This problem can be done by using not so simple integration techniques
c.f. Advanced Calculus, Buck, 1965, pp214-219:

wherein: and are derived.
Now induction on n would lead to the solution.

My solution uses integration by parts once:

Spoiler:

Now integration by parts yields:

Thus

Funny what the brain conjures while one bikes 1 1/2 hours on a cold day!
Correction:

per commutative's observation the last two lines should have been:

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Last edited by robbwrr on Fri, 26 Dec 2008 22:25:54 UTC, edited 1 time in total.

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 Post subject: Posted: Fri, 26 Dec 2008 09:56:14 UTC
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robbwrr wrote:

My solution uses integration by parts once:

Spoiler:

Now integration by parts yields:

Thus

Funny what the brain conjures while one bikes 1 1/2 hours on a cold day!

nice work! except that your final answer is actually instead of that, of course, is not important.

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