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MathGroup Archive 1997

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Re: Another Bug in Mathematica 3.0.0 definite integration

  • To: mathgroup at
  • Subject: [mg9206] Re: Another Bug in Mathematica 3.0.0 definite integration
  • From: "Gregor Overney" <overney at>
  • Date: Tue, 21 Oct 1997 02:03:19 -0400
  • Sender: owner-wri-mathgroup at

Mathematica would give you at least a warning, suggesting to
carefully check the convergence.

your input produces:

Integrate::gener: Unable to check convergence

and N[a] gives the obviously wrong value of -3.0123622967174799.


luca ciotti wrote in message <624fv1$les at>...
>Dear Users,
>unfortunately I found another erroneous result in  a definite integral
>in Mathematica 3.0.0
>        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]
>     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).
>luca ciotti
>osservatorio astronomico di bologna
>via zamboni 33, 40126 bologna (italy)

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