Re: binomial expansion of a fraction power

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 02/27/05 

Date: Sun, 27 Feb 2005 13:05:03 -0700

In article <20050227144135.206$5r@newsreader.com>,
 David W. Cantrell <DWCantrell@sigmaxi.org> wrote:

> Virgil <ITSnetNOTcom#virgil@COMCAST.com> wrote:
> > In article <20050227085722.234$ob@newsreader.com>,
> > David W. Cantrell <DWCantrell@sigmaxi.org> wrote:
> >
> > > zyf <zhangyunfeng@gmail.com> wrote:
> > > > How to do a binomial expansion to the equation below?
> > > >
> > > > P(x,t) r-1 v pow
> > > > ------- = ( 1 + ----- * ---- )
> > > > P0 2 a0
> > > >
> > > > where 'pow' is a fraction number.
> > > >
> > > > This equation is said may be expansion to third-order form, anybody
> > > > know how to?
> > >
> > > Use equation (2) or one of the following equations at
> > > <http://mathworld.wolfram.com/BinomialSeries.html>.
> > >
> > > BTW, I don't like the opening sentence in that MathWorld entry: "The
> > > binomial series is the finite sum ..." As I recall, the term "binomial
> > > series" is most often used when the expansion is _not_ finite.
> >
> > I can't say whether "most often" is correct, but the series is
> > certainly _not_finite_ frequently enough to falsify the MathWorld entry.
>
> Agreed (and so I'm sending a copy of this to Eric Weisstein).
>
> > A word of caution,however!
> > The expansion for '(1+x)^pow' only converges when x is less than 1 in
> > absolute value, and only converges rapidly when x is close to zero, the
> > closer, the faster.
>
> Well, to be picky, it also converges when |x| = 1 if pow > 0.
>
> David

In Mathematics, picky is good.

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