Re: Troubles with Integrating certain functions in 5.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg49132] Re: [mg49113] Troubles with Integrating certain functions in 5.0*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 2 Jul 2004 02:01:40 -0400 (EDT)*References*: <200407010926.FAA21090@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 1 Jul 2004, at 18:26, Matt Hancher wrote: > > Hi all, > > I'm running 5.0.0.0 on OS X, and Integrate is misbehaving. Below I > show > the results of performing the same definite integral two times. The > only > difference is that I pulled out the constant factor Sqrt[E] in the > second > case. Only the second case is correct; the Struve function shouldn't > be > there in the first case. > > I'm pretty sure I'm not just being dumb. Anybody have any thoughts? > I'd be curious to know how this plays out with other versions and on > other platforms.... > > In: Integrate[Exp[-Sin[x]^2]*Sqrt[E], {x, 0, Pi}] > Out: Pi ( BesselI[0, 1/2] - StruveL[0, 1/2] ) > > Versus: > > In: Integrate[Exp[-Sin[x]^2], {x, 0, Pi}]*Sqrt[E] > Out: Pi BesselI[0,1/2] > > Thanks for any thoughts, > Matt > > Matt Hancher > NASA Ames Research Center > Official: mdh at email.arc.nasa.gov > Personal: mdh at media.mit.edu > > Version 4.2 gives the right answer: Integrate[E^(-Sin[x]^2), {x, 0, Pi}] (Pi*BesselI[0, 1/2])/Sqrt[E] This is on Mac OS X but I am pretty sure that the behaviour of both version 4.2 and 5.0 is the same in this respect on both platforms. I do not have 5.01 so I am not sure if this problem is still present. Mathematica 5.0 introduced some pretty radical changes in the way Integrate works. Many bugs have been fixed (though naturally one rarely hears of this). Partly as a result of these fixes and partly due the more ambitious approach in version 5, a substantial number of new bugs have also been created. At the moment it seems to me that the best thing to do is to use use both versions (it is possible to line two Kernels to the same front end) and also check the answer with NIntegrate, which is very reliable. Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Troubles with Integrating certain functions in 5.0***From:*mdh@media.mit.edu (Matt Hancher)