[Date Index]
[Thread Index]
[Author Index]
A question about N[...]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89395] A question about N[...]
*From*: "wyelen at gmail.com" <wyelen at gmail.com>
*Date*: Sun, 8 Jun 2008 02:32:28 -0400 (EDT)
Recently I came across a puzzling problem which I believed to be
related to the function N.
My platform is Mathematica 6.0 for Microsoft Windows (32-bit). When
calculating the following
integral, I got different results from Integrate & NIntegrate:
In[1]:= Integrate[BesselJ[0, 2.405 * r]^2, {r, 0, 20}]
Out[1]= 0.
In[2]:= NIntegrate[BesselJ[0, 2.405 * r]^2, {r, 0, 20}]
Out[2]= 0.864755
Guessing a problem caused by numerical number 2.405, I rewrote it as
an exact number:
In[3]:= Integrate[BesselJ[0, (2 + 405/1000)*r]^2, {r, 0,
20}]
Out[3]= 20*HypergeometricPFQ[{1/2, 1/2}, {1, 1, 3/2}, -
(231361/100)]
then evaluated the numerical value, which was surprisingly still 0.:
In[4]:= N[%]
Out[4]= 0.
but evaluating with 6-digit precision gave the same result as
NIntegrate:
In[5]:= N[%%,6]
Out[5]= 0.864755
In help page for N it said "N[expr] is equivalent to
N[expr,MachinePrecision]", but evaluating with a
approximate precision didn't gave 0.:
In[6]:= N[MachinePrecision]
Out[6]= 15.9546
In[7]:= N[%3,15.9546]
Out[7]= 0.8647551857405188
I wonder is this caused by the function N ,or whether I should just
turn to another OS (say Linux) and things will go well.
Thanks a lot for your reply!
Prev by Date:
**Re: Instructions in for**
Next by Date:
**Re: Instructions in for**
Previous by thread:
**Re: ListAnimate or movie with No AppearanceElements**
Next by thread:
**Re: A question about N[...]**
| |