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) >