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Re: Error function integral / Wolfram Function reference
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126000] Re: Error function integral / Wolfram Function reference
*From*: danl at wolfram.com
*Date*: Thu, 12 Apr 2012 02:35:03 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <jlmefo$m7d$1@smc.vnet.net>
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
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