Re: Strange results from Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg75012] Re: Strange results from Mathematica
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sat, 14 Apr 2007 01:06:23 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <evn8cr$s7$1@smc.vnet.net>
Jung-Tsung Shen wrote:
> Hi, I encountered a rather strange results from Mathematica today.
>
> When evaluating the following integration
>
> (1) Integrate[x (BesselJ[0, x])^2, {x,0, infinity}]
==========================================^^^^^^^^^
Spelling error: infinity must be written Infinity (with a capital I)
> my Mathematica gave the answer 0. That's very weird, since if you plot
> out the function x (BesselJ[0, x])^2, apparently the integral should
> not be zero ...
You are right since this integral is divergent. Mathematica 5.2 for
Microsoft Windows (June 20, 2005) returns
Integrate[x*BesselJ[0, x]^2, {x, 0, Infinity}]
Integrate::"gener" : "Unable to check convergence. More...
Integrate::"idiv" : "Integral of (x*\"BesselJ[0, x]\"^2) does not
converge on ({0, Infinity}). More...
Integrate[x*BesselJ[0, x]^2, {x, 0, Infinity}]
You could try the following tho check the limit:
In[7]:=
Integrate[x*BesselJ[0, x]^2, {x, 0, t}]
Out[7]=
1 2 2
- t (BesselJ[0, t] +
2
2
BesselJ[1, t] )
In[8]:=
Limit[%, t -> Infinity]
Out[8]=
Infinity
> Moreover, for the following integration
>
> (2) Integrate[ (BesselJ[0, x])^2, {x,0, infinity}]
>
> My Mathematica says it's some finite value. However, once you did
> this, and then did (1), and then came back to do (1), the answer
> became 0 ...
Not sure what you mean here. On my system, the expression is just
returned unevaluated.
In[9]:=
Integrate[BesselJ[0, x]^2, {x, 0, Infinity}]
Out[9]=
Integrate[BesselJ[0, x]^2, {x, 0, Infinity}]
> My Mathematica version is 5.0.1.0 on Mac Powerbook.
>
> Thanks.
>
> JT
>