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MathGroup Archive 1997

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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)


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