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Re: Error function integral / Wolfram Function reference

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126098] Re: Error function integral / Wolfram Function reference
  • From: danl at wolfram.com
  • Date: Tue, 17 Apr 2012 06:03:30 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jlmefo$m7d$1@smc.vnet.net> <jm64k8$6ll$1@smc.vnet.net> <jmgr3f$pg2$1@smc.vnet.net>

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



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