• To: mathgroup at smc.vnet.net
• Subject: [mg89417] Re: [mg89395] A question about N[...]
• From: "W_Craig Carter" <ccarter at mit.edu>
• Date: Mon, 9 Jun 2008 02:27:24 -0400 (EDT)
• References: <200806080632.CAA02634@smc.vnet.net>

```Hello,
I believe there is a bug AND and problem with the documentation for N[].

>From the documentation:
"N[expr] is equivalent to N[expr,MachinePrecision]. " While
technically correct for this example,
I believe that ought to be \$MachinePrecision.

v = 20*HypergeometricPFQ[{1/2, 1/2}, {1, 1, 3/2}, -(231361/100)]

N[v]       (* 0. *)
N[v, MachinePrecision]        (* 0. *)
N[v, \$MachinePrecision]         (* 0.8647551857405188 *)

Table[N[v, i], {i, 1, 50}] // TableForm

On Sun, Jun 8, 2008 at 2:32 AM, wyelen at gmail.com <wyelen at gmail.com> wrote:
>
> 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.
>
>
>

--
W. Craig Carter

```

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