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Re: Error function integral / Wolfram Function reference

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126376] Re: Error function integral / Wolfram Function reference
  • From: Donagh Horgan <donagh.horgan at gmail.com>
  • Date: Sat, 5 May 2012 04:12:04 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jlmefo$m7d$1@smc.vnet.net> <jm64k8$6ll$1@smc.vnet.net>

On Tuesday, April 17, 2012 11:04:11 AM UTC+1, da... at wolfram.com wrote:
> On Monday, April 16, 2012 5:08:47 AM UTC-5, Donagh Horgan wrote:
> > On Thursday, April 12, 2012 9:43:52 AM UTC+1, da... at wolfram.com wrote:
> > > On Friday, April 6, 2012 4:54:00 AM UTC-5, Donagh Horgan wrote:
> > > > Hello,
> > > > 
> > > > I'm trying to integrate the following function in Mathematica, but I'm
> > > > not having much success:
> > > > 
> > > > http://functions.wolfram.com/06.25.21.0016.01
> > > > 
> > > > I am using the command Integrate[z^n E^(b z) Erf[a z], z], but
> > > > Mathematica gives up and does not return the above result, and instead
> > > > returns the command itself. If I tell Mathematica to assume that n is
> > > > a natural number (Integrate[z^n E^(b z) Erf[a z], z, Assumptions ->
> > > > {Element[n, Integers], n >= 0}]), as specified at the above Wolfram
> > > > Functions page, I get the same result.
> > > > 
> > > > For the specific problem I am looking at, a < 0 and b < 0 and both are
> > > > real. However, even under these assumptions, the integral does not
> > > > compute in Mathematica.
> > > > 
> > > > The question I have, then, is whether Mathematica should be able to
> > > > compute this result, i.e. are all the results on the Wolfram Functions
> > > > website included in Mathematica? If so, then why does the above
> > > > integral not compute? If not, is there a complete list of identities
> > > > on the Wolfram Functions site which Mathematica does (or,
> > > > equivalently, does not) recognize?
> > > > 
> > > > Regards,
> > > > Donagh Horgan
> > > 
> > > That's not a "closed form" result. it is expressing the integral as a nested sum.
> > > 
> > > Daniel Lichtblau
> > > Wolfram Research
> > 
> > Hi Daniel,
> > 
> > Thanks for your help. From your reply, am I correct in assuming that Mathematica will attempt to substitute only closed form solutions for integrals?
> 
> That is, to the best of my knowledge, correct. In the case of multiple integrals it will in some cases give results with some of them unevaluated.
> 
> 
> > I had previously assumed (albeit with no evidence) that Mathematica had a "knowledge" of all the identities on the Wolfram Functions site. Can you confirm this? It would save me a good deal of time with symbolic calculations in the future.
> > 
> > Many thanks,
> > Donagh
> 
> Offhand I do not know the extent to which functions.wolfram.com knowledge is built into Mathematica.
> 
> Daniel Lichtblau
> Wolfram Research

Great, thanks for all your help!



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