bugs in Mathematica 5.1

*To*: mathgroup at smc.vnet.net*Subject*: [mg54032] bugs in Mathematica 5.1*From*: "Gennady Stupakov" <stupakov at yahoo.com>*Date*: Tue, 8 Feb 2005 05:31:09 -0500 (EST)*Reply-to*: "Gennady Stupakov" <stupakov at yahoo.com>*Sender*: owner-wri-mathgroup at wolfram.com

I tried to post this a few days ago, but it looks like it did not make it. Here is a couple of bugs that I found recently in Mathematica 5.1. In[13]:={$System, $Version, $MachineType, $ProcessorType} Out[13]={"Microsoft Windows","5.1 for Microsoft Windows (October 25, 2004)", "PC", "x86"} First, I integrate E^(I*x^2), from 0 to Infinity and get zero, which, of course, is wrong. In[1]:={Integrate[E^(I*x^2), {x, 0, Infinity}], Integrate[Cos[x^2] + I*Sin[x^2], {x, 0, Infinity}]} Out[1]={0, (1/2 + I/2)*Sqrt[Pi/2]} Second is a more complicated integral that I recently encounted in my research. In[2]:=Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi}, GenerateConditions -> True] Out[2]=If[Re[a] < Re[b], 2*Pi*BesselI[0, -a + b], Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi},Assumptions -> Re[a] >= Re[b]]] Let us check this result comparing it with numerical integration for, say, b=2 and a=1: In[3]:= b = 2.; a = 1.; {Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi}], NIntegrate[E^(a*Cos[x] + b*Cos[2*x]), {x, 0, 2*Pi}]} Out[5]={7.95493, 20.8711} Again, the analytical result is wrong. It would be interesting if those bugs are reproduced on other OS and/or versions of Mathematica. Gennady.

**Follow-Ups**:**Re: bugs in Mathematica 5.1***From:*"Igor C. Antonio" <igora@wolfram.com>

**Re: bugs in Mathematica 5.1***From:*Murray Eisenberg <murray@math.umass.edu>