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Question: Hyper geometric functions

Question:Hyper geometric functions

amrramadaneg 76
integral
January 28 2012
0 
Hi,  I have and integral its results contains Beta function and hypergeometric function.
I found a difficulty to program the hypergeometric function with Maple 13.    is any one can solve this problem
where

 

∫₀^{(π/2)}((sin^{α}xcos^{β}x)/(√(1-k²sin²x)))dx=(1/2)B(((α+1)/2),((β+1)/2))F(((α+1)/2),(1/2);((α+β+2)/2);k²),α>-1,β>-1,∣k∣<1

The problem in written the following function       F(((α+1)/2), (1/2); ((α+β+2)/2); k²)

 

 
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