| Author |
Comment/Response |
Kyung-Taek Lim
|
 10/01/00 08:03am
Version Number: 4.0.1.0
Platform: Windows 2000 Professional
Registered Name: Kyung-Taek_Lim
Organization: Brown
License ID: L2962-6007
Mathematica gives different results for the same integrals, depending on whether I use x^2-1 or (x-1)(x+1) in the integrand, or depending on the integration variable.
In[1]:= Integrate[Sqrt[-(-1/(4x(x^2-1)))],{x,1,infinity}]
Out[1]= Sqrt[Pi] Gamma[5/4] / Gamma[3/4]
The next cell is the same integral as the above integral, because (x^2-1)=(x-1)(x+1). However, Mathematica produces different result.
In[2]:= Integrate[Sqrt[-(-1/(4x(x-1)(x+1)))],{x,1,infinity}]
Out[2]= -i EllipticF[ComplexInfinity,2]
Now let't perform change of variable.
Y=x-1
dY=dx
If x=1, Y=0.
As x->infinity, Y->infinity.
Mathematica produces still different result.
In[3]:=Integrate[Sqrt[-(-1/(4(Y+1)(Y)(Y+2)))],{Y,0,infinity}]
Out[3]:=0
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