       a definite integral

• To: mathgroup at smc.vnet.net
• Subject: [mg83806] a definite integral
• From: "Arnold Knopfmacher" <Arnold.Knopfmacher at wits.ac.za>
• Date: Sat, 1 Dec 2007 05:40:11 -0500 (EST)

Given the function

f=(1 - z - u*z - Sqrt[-4*z + (1 + z - u*z)^2])/
(2*u*z*Sqrt[-4*z + (1 + z - u*z)^2])

I wish to compute
g[z]=Integrate[f,{u,0,1}]

(Here  z and u are independent variables, that are real and positive and
the function inside of Sqrt[ ] is nonnegative.)

Mathematica 5.2 can only evaluate this if I ask for the indefinite integral
but this then gives errors when u=0 or u=1 is substituted. I believe
it is because
Mathematica is choosing the wrong branches of the square root or of the Log
function when it computes the indefinite integral.=0D

The function f is integrable, as can be obseved by first finding say
Series[f,{z,0,10}] and then integrating term by term to find the (correct)
initial power series terms of g[z].

Thanks
Arnold Knopfmacher

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