Re: Another Bug in Mathematica 3.0.0 definite integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg9254] Re: Another Bug in Mathematica 3.0.0 definite integration*From*: carlos at mars.Colorado.EDU (Carlos A. Felippa)*Date*: Fri, 24 Oct 1997 01:01:07 -0400*Organization*: University of Colorado, Boulder*Sender*: owner-wri-mathgroup at wolfram.com

In article <62hfha$m06$4 at dragonfly.wolfram.com> "Gregor Overney" <overney at worldnet.att.net> writes: >Mathematica 3.0.1.1x would give you at least a warning, suggesting to >carefully check the convergence. > >your input produces: > >Integrate::gener: Unable to check convergence > >and N[a] gives the obviously wrong value of -3.0123622967174799. > >GTO > > >luca ciotti wrote in message <624fv1$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. >> This is a pattern I have observed in many integrals involving trigonometric functions that lead to hypergeometric and/or elliptic functions. The time comparison of 2.2 vs 3.0 is interesting. Results from Mathematica 2.2.1 on above test function: (Pi^(1/2)*Gamma[1/4])/(2*2^(1/4)*Gamma[3/4]) - 2*Hypergeometric2F1[1/2, 1, 5/4, -1] + Hypergeometric2F1[3/4, 1, 3/2, -1] 1.397395299268851 Time: 0.95 seconds on Mac 8500/120. Results from Mathematica 3.0.1, same machine: -2*2^(3/4)*HypergeometricPFQ[{1/4, 3/4}, {5/4}, -1] -3.012362296717479 Time: 10.4 seconds, a factor of 10. Both 3.0 and 3.0.1 give the warning about convergence.