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Teach
Posts:
278
Registered:
12/6/04
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Re: An extention of the binomial theorem
Posted:
Mar 30, 1997 5:27 AM
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israel@math.ubc.ca (Robert Israel) wrote:
>In article <333b2a54.2985719@news.netvision.net.il>,
>Itai <alonig@netvision.net.il> wrote:
>>is there an extention of the binomial theorem to (a+b)^x where x is a
>>real number?if ther is one,i'd like to know what it is.
>>
>Yes, it's called the binomial series.
>(a+b)^x =sum_{n=0}^infinity C(x,n) a^(x-n) b^n for |b| < a
I think you still have the "Binomial Theorem" here.
There *is* an extension, and it is called the "Multinomial" Theorem.
By that is meant (a + b + c + ....)^n. The concept relies upon the
same principles of development as the Binomial series; that is, one
considers how many ways the variables may be joined, in order to get
the coefficients of the series.
See Hall and Knight, "Higher Algebra" for one source.
David.
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