Re: more wrong integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg24517] Re: more wrong integrals*From*: Hendrik van Hees <h.vanhees at gsi.de>*Date*: Mon, 24 Jul 2000 03:04:01 -0400 (EDT)*References*: <8l685l$s8l@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

It seems indeed that Mathematica 4.0's Integrate has a lot of shortcomings and as shown here some serious bugs. I don't know wether Wolfram Research is really caring about this Newsgroup. On my opinion these are really bugs and should be corrected free of charge for all users of Mathematica 4.0, for instance through downloadable bug fixes from Wolfram's ftp-servers. Some time ago I mentioned some problems concerning (relatively simple) integrals which are typical for radiation correction calculations ("Feynman diagrams") in high energy particle physics. For the experts: I calculated simple one-loop integrals with dimensional regularisation (by hand of course) and let Mathematica do the remaining finite integrals over the Feynman parameter(s). The problem with these integrals is that Mathematica gets out in principle the correct result but does not care about the assumptions made for the parameters of the integral. Especially putting the external momenta to the euclidean region does not ensure the reality of the calculated diagrams which is due to the wrong choice of the Riemann sheet. The only way out is to use Mathematica only for finding the indefinite integral then setting by hand the functions to the right sheets (there is a nice table about the definition of the built in functions concerning the branch cuts and so on somewhere in MathSource). Concerning your two examples Mathematica 3.0 is better than 4.0 because it states correctly that these integrals are not convergent. -- Hendrik van Hees Phone: ++49 6159 71-2751 c/o GSI-Darmstadt SB3 3.183 Fax: ++49 6159 71-2990 Planckstr. 1 mailto:h.vanhees at gsi.de D-64291 Darmstadt http://theory.gsi.de/~vanhees/index.html