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!