Standard Beta Function

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1 total messages Started by Peyman Milanfar Mon, 11 Jan 1993 20:03

#182

Author: Peyman Milanfar
Date: Mon, 11 Jan 1993 20:03

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I have a sort of mundane question.
Let the standard Beta function be defined by

B(\frac{a+1}{2},\frac{b+1}{2})=
 2 \int_{0}^{\pi/2}\sin^a(\theta)\cos^b(\theta)d\theta.

I need a tight upper and lower bounds on $B$ when $a$ and $b$ are even positive
integers. A very simple upper bound in this case is B((a+1)/2,(b+1)/2) < \pi .
I need something stronger.
Any references to the literature, etc. is appreciated.

Thanks
Peyman Milanfar

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