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