Re: Another Bug in Mathematica 3.0.0 definite integration
- To: mathgroup at smc.vnet.net
- Subject: [mg9206] Re: Another Bug in Mathematica 3.0.0 definite integration
- From: "Gregor Overney" <overney at worldnet.att.net>
- Date: Tue, 21 Oct 1997 02:03:19 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica 3.0.1.1x 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.
GTO
luca ciotti wrote in message <624fv1$les at smc.vnet.net>...
>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)
>