Path: ccsf.homeunix.org!ccsf.homeunix.org!news1.wakwak.com!nf1.xephion.ne.jp!onion.ish.org!gcd.org!news.yamada.gr.jp!newsfeed.media.kyoto-u.ac.jp!headwall.stanford.edu!newsfeed.stanford.edu!logbridge.uoregon.edu!arclight.uoregon.edu!news.purdue.edu!not-for-mail From: hrubin@odds.stat.purdue.edu (Herman Rubin) Newsgroups: sci.math.symbolic,comp.soft-sys.math.maple,sci.math,fj.sci.math Subject: Re: An exact 1-D integration challenge - 3 Date: 5 Feb 2005 10:31:44 -0500 Organization: Purdue University Statistics Department Lines: 32 Message-ID: References: <1107555276.418478.215730@f14g2000cwb.googlegroups.com> <1107559162.508814.123220@f14g2000cwb.googlegroups.com> NNTP-Posting-Host: odds.stat.purdue.edu X-Trace: mailhub227.itcs.purdue.edu 1107617504 17676 128.210.141.13 (5 Feb 2005 15:31:44 GMT) X-Complaints-To: news@purdue.edu NNTP-Posting-Date: Sat, 5 Feb 2005 15:31:44 +0000 (UTC) Xref: ccsf.homeunix.org fj.sci.math:1614 In article <1107559162.508814.123220@f14g2000cwb.googlegroups.com>, Vladimir Bondarenko wrote: >isr...@math.ubc.ca (Robert Israel) writes on Feb 4, 2:39 pm >With a serene look, I continue, What then about the following >integral >int(erf(z)*exp(z^2-z^4), z= 0..infinity); >? >If you would not be able to get to the answer here, Is there a >person who can find the exact value of this integral? I have not summed the series of expression, but it can be done in the following manner: The not sufficiently well known expansion of exp(z^2)*erf(z) is C*(z + 2*z^3/3 + 2^2*z^5/(3*5) + 2^3*z^7/(3*5*7) + ... ) This being a series of positive terms, it can be integrated term by term. It is certainly expressible in terms of hypergeometric functions. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558