From: SourceForge.net <no...@so...> - 2012-01-03 19:45:41
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Bugs item #3469184, was opened at 2012-01-03 11:45 Message generated for change (Tracker Item Submitted) made by woollett You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3469184&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Ted Woollett (woollett) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(exp(-x^n),x,0,1) bug for n >2 Initial Comment: the definite integral of the real function exp(-x^n) over the real interval (0,1) is broken (spurious imaginary parts, wrong real parts) for n = 3 through 15, and probably forever. ----------------------------------------------------------------- (%i1) exp_test(n) := ( print (n," qags = ", first( quad_qags (exp(-x^n),x,0,1)), " integrate = ", expand(float(rectform(integrate(exp(-x^n),x,0,1))))))$ (%i2) for m thru 15 do exp_test(m)$ 1 qags = 0.63212055882856 integrate = 0.63212055882856 2 qags = 0.74682413281243 integrate = 0.74682413281243 3 qags = 0.80751118213967 integrate = 0.69932519757296*%i-0.40375559106984 4 qags = 0.8448385947571 integrate = 0.8448385947571*%i 5 qags = 0.87007466768589 integrate = 0.82749018236601*%i+0.26886785869008 6 qags = 0.88826369875194 integrate = 0.76925892837871*%i+0.44413184937597 7 qags = 0.90199160301324 integrate = 0.70520543215755*%i+0.56238256584096 8 qags = 0.91271857185875 integrate = 0.64538949147622*%i+0.64538949147622 9 qags = 0.9213308364909 integrate = 0.59222004611848*%i+0.70578036756801 10 qags = 0.92839720283799 integrate = 0.54569818409775*%i+0.7510891146261 11 qags = 0.93429939205577 integrate = 0.5051203870693*%i+0.78598266428894 12 qags = 0.93930307080183 integrate = 0.46965153540091*%i+0.81346032116712 13 qags = 0.94359882032526 integrate = 0.43851223691831*%i+0.83551526125626 14 qags = 0.94732690220079 integrate = 0.41102973849353*%i+0.85351204660935 15 qags = 0.95059283193 integrate = 0.38664093739113*%i+0.86840976367727 ------------------------------------------------ Maxima version: 5.25.1 Maxima build date: 10:2 9/6/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 Ted Woollett ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3469184&group_id=4933 |