Re: [Mathematica 5.1] Bug Report - Two numerical values for a same variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg54189] Re: [Mathematica 5.1] Bug Report - Two numerical values for a same variable*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Sat, 12 Feb 2005 01:59:14 -0500 (EST)*References*: <cuhr4q$978$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ling Li <ling at caltech.edu> wrote: > Hi, > > Mathematica v5.1 is much better than v5.0 on the accuracy of > integration. I am not talking about numerical accuracy---v5.0 sometimes > gives out two answers that are off by a constant for the same input. > > However, I still get two different numerical values for a same variable > in v5.1 > > a=Exp[Integrate[(Cos[w]-Exp[-w^2/2]*Cos[23/100*w])/w, {w, 0, Infinity}]] > N[a] > N[a,20] (Note: I'm still using v5.0) This is interesting, and seems to be a true bug. I hope that you have (or will) report it to user support. In[265]:= Exp[Integrate[(Cos[w] - Exp[-w^2/2]*Cos[(23/100)*w])/w, {w, 0, Infinity}]] Unable to check convergence. Out[265]= E^((1/2)*(-Log[2] - Derivative[1, 0, 0][Hypergeometric1F1][0, 1/2, -(529/20000)])) In[266]:= N[%] Out[266]= 0.7258911870047994 In[267]:= N[%%, 20] Out[267]= 0.7071067811865475244008443621049178777`20. Note that the above is 1/Sqrt[2], which is precisely what we'd get if the derivative of the hypergeometric function were 0. But it's not: In[268]:= N[Derivative[1, 0, 0][Hypergeometric1F1][0, 1/2, -(529/20000)], 20] Out[268]= -0.05243686946160788253943021003866848941`20. In[269]:= E^((1/2)*(-Log[2] - %)) Out[269]= 0.72589118700480243184501059813946795275`21.141234767758785 and so Out[266] was correct. Why did Mathematica think that the derivative was 0 when getting Out[267] but not when getting Out[268]? David Cantrell