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MathGroup Archive 2012

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Error function integral / Wolfram Function reference

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125887] Error function integral / Wolfram Function reference
  • From: Donagh Horgan <donagh.horgan at gmail.com>
  • Date: Fri, 6 Apr 2012 05:52:51 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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



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