A bug of Integrate[] in Mathematica 4.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg27343] A bug of Integrate[] in Mathematica 4.1*From*: Rino Bandiera <bandiera at arcetri.astro.it>*Date*: Wed, 21 Feb 2001 03:17:26 -0500 (EST)*Organization*: Osservatorio Astrofisico di Arcetri*Sender*: owner-wri-mathgroup at wolfram.com

Hi! While Mathematica 4.1 correctly solves the Integral: Integrate[1 - x^a, {x, 0, 1}] a ---- 1 + a it gets stuck with an Integral like: Integrate[1 - x^(-9999/10000), {x, 0, 1}] (i.e. an exponent close to -1, but as a fraction of 2 large integer numbers) Mathematica 3.0, instead, was working well on this point. A related problem is for definite integrals like: Integrate[1 - x^((5 - q)/2), {x, 0, 1}] Here, while Mathematica 3.0 did not check on the allowed interval for the parameter q, Mathematica 4.1 does, but giving incorrect results. In fact the quote interval of validity is: Re[q]<2 (while it should clearly be: Re[q]]<7) Odd results come out for all this class of functions. ------------- I have reported the problem to the Wolfram Support. The only result I got are the following answers: > Thank you for the report. Integrate[] appears to be behaving erroneously in > all of the cases you present. I have notified the the developers of the > problems. Unfortunately, there does not appear to be a workaround. > Unfortunately, there are no bug lists available, and I will not be informed > of the status of the bug until it is fixed. Most likely, a patch will not be > made available. Therefore, no solution is on the way, unfortunately. JUST BE CAREFUL! Best regards, Rino