Re:More gaussian integration bugs

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re:More gaussian integration bugs*From*: ross at macadam.mpce.mq.edu.au*Date*: Fri, 10 Apr 1992 16:21:56 +1000

This one is a doosie. At our site the answer varies according to the version of Mathematica used: $Version DEC_RISC 2.0 (August 23, 1991) Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}] 3 3 -(2 E Sqrt[Pi] + HypergeometricU[-, -, 1]) 2 2 ------------------------------------------ 2 E Integrate[Exp[-x^2],{x,-Infinity,Infinity}] Sqrt[Pi] N[%2] -1.86153 N[%3] 1.77245 ---------------------------------------------------------------------------- ----------------- $Version DEC RISC (ULTRIX) 1.2 (January 24, 1990) Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}] Sqrt[Pi] Integrate[Exp[-x^2],{x,-Infinity,Infinity}] Sqrt[Pi] N[%2] 1.77245 N[%3] 1.77245 ---------------------------------------------------------------------------- ----------------- $Version Macintosh 2.0 (December 12, 1991) Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}] 3 3 -(2 E Sqrt[Pi] + HypergeometricU[-, -, 1]) 2 2 ------------------------------------------ 2 E Integrate[Exp[-x^2],{x,-Infinity,Infinity}] Sqrt[Pi] N[%2] -1.86153 N[%3] 1.77245 ---------------------------------------------------------------------------- ----------------- The three different kernels were all tested from the same Macintosh front-end. Switching kernels is just a menu-selection --- Well done, Theo Gray and Doug Stein!! (The only problem is that the Integration packages on the Mac take 5 minutes to load, using my Mac IIci, with a 5MB memory partition for Mathematica. ) The latter result above is surprising, since Paul McGuire (pmcguire at bucknell.edu) got the correct answer with version 2.0 on a Mac IIcx. I have tried to use Trace on this integral, in an attempt to follow the use of functions from the Integrate package, but all I get is the final answer, once the integrand has been put into a normal form. Setting TraceForward->True and TraceInternal->True did not help. Would someone please shed some light on how to use Trace effectively here. _______________________________ Ross Moore | Mathematics Dept | Macquarie University | North Ryde, Sydney | Australia | | ross at macadam.mpce.mq.edu.au | ______________________________|