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MathGroup Archive 1996

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help: Integrate[(1-x)^(-1/2)*(1-y)^(-1/2)/(x+y),{x,0,1},{y,0,1}]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4778] help: Integrate[(1-x)^(-1/2)*(1-y)^(-1/2)/(x+y),{x,0,1},{y,0,1}]
  • From: oekelly at riemann.rice.edu (Owen Ernest Kelly)
  • Date: Fri, 13 Sep 1996 13:54:57 -0400
  • Organization: Rice University
  • Sender: owner-wri-mathgroup at wolfram.com

Would someone let me know if they have a solution for the
following?

Integrate[(1-x)^(-1/2)*(1-y)^(-1/2)/(x+y),{x,0,1},{y,0,1}]

I'm intersted if Mathematica 3.0 can do it.
MMA2.2 cannot do that one, but does provide an answer for the more general problem

Integrate[(x*y)^(1/2)/(x+y)* x^(a-1/2) *(1-x)^(b-1/2) *y^(c-1/2) *(1-y)^(d-1/2),
{x,0,1},{y,0,1}]

however that answer appears to be incorrect.  I'm interested in the
case that a,b,c,d are non-negative integers. The first integral is for a=b=c=d=0.

I expect the answer will be in terms of hypergeometric functions and beta functions.

I am at oekelly.rice.edu, but I will follow 
these threads for a few days too.
I appreciate any help or suggestions.

Best regards,

Owen Kelly
-----------------------------------------------
Department of Electrical & Computer Engineering 
MS366, Rice University, Houston, TX, USA, 77005
(713) 527-8101 x2209  or  527-8750 (beep) x2209


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