Re: Re: How to treat this false singular point?

• To: mathgroup at smc.vnet.net
• Subject: [mg68458] Re: [mg68455] Re: How to treat this false singular point?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 6 Aug 2006 02:56:28 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```f[x_, xList_List] := Module[
{y = Complement[xList, {x}]},
Total[(x - y)*Log[Abs[x - y]]]];

xList=Range[5];

Plot[f[x,xList],{x,-1,5},
Epilog->{Red ,AbsolutePointSize[4],
Point/@({#,f[#,xList]}&/@xList)}];

Bob Hanlon

---- simon yang <yanshanguke at 163.com> wrote:
> In: Limit[(x-10)*Log[Abs[x-10]],x->10]
> Out: 0
>
>
>
> Bob Hanlon wrote:
> > f[x_, xList_List] := Total[(x-xList)*Log[Abs[x-xList]]];
> >
> > f[x, {x1, x2, x3}]
> >
> > (x - x1)*Log[Abs[x - x1]] + (x - x2)*Log[Abs[x - x2]] + (x - x3)*Log[Abs[x - x3]]
> >
> > a singularity will exist for each value of x in xList; therefor, f[xn, xList] cannot have the value 1
> >
> > f[5. - 10^-15, Range[5]]
> >
> > 10.2273
> >
> > Plot[f[x,Range[5]],{x,-1,5}];
> >
> >
> > Bob Hanlon
> >
> > ---- simon yang <yanshanguke at 163.com> wrote:
> > > Dear everyone,
> > > I have a function:
> > > f[x_]:=(x-x1)Log[Abs[x-x1]] + (x-x2)Log[Abs[x-x2]] + ... +
> > > (x-xn)Log[Abs[x-xn]],
> > > {x1,x2,...,xn}={100,200,300,...} for instance
> > > How to get value: f[x] as there are different singular at different x?
> > > I know at x=xn, f[x]==1, But Mathematica return: "Indeterminate", What
> > > should I do?
> > >  what others do in C++, Fortran ?
> > >
>

```

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