Another Bug in Mathematica 3.0.0 definite integration
- To: mathgroup at smc.vnet.net
- Subject: [mg9147] Another Bug in Mathematica 3.0.0 definite integration
- From: luca ciotti <ciotti at boas5.bo.astro.it>
- Date: Thu, 16 Oct 1997 03:37:50 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Dear Users,
unfortunately I found another erroneous result in a definite integral
in Mathematica 3.0.0
Let
a=Integrate[1/Sqrt[Sin[x]+Cos[x]], {x,0,Pi/2}]
(Note that the integrand is definite positive in the integration range)
Mathematica3.0.0 returns
a= -2 2^(3/4) HypergeometricPFQ[{1/4,3/4},{5/4},-1]
and
N[a]=-3.01236...
With the standard change of variable t=Tan[x/2] the integral can be
easily evaluated symbolically, and then the numeric evaluation returns
1.3974.....
in perfect agreement with the result obtained performing directly
NIntegrate on the original integrand.
I understand that it can be difficult taking in the due account branch
points in the complex plane, but I think that even this could be a
"technical" explanation for the behavior, the behavior is *still*
wrong. I wonder why during the development of Mathematica 3.0.0 such
silly experiments apparently have not be done! (I'm not at all a
mathematician, but with simply experiments I hade already found 3
different bugs).
regards,
luca ciotti
osservatorio astronomico di bologna
via zamboni 33, 40126 bologna (italy)