Talk:Binomial series

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: Start Class High Priority  Field: Analysis

[edit] Inconsistency

{\alpha \choose k} = \frac{\alpha (\alpha-1) (\alpha-2) \cdots (\alpha-k+1)}{k!}=\frac{(-1)^k}{k!}(-\alpha)_k,

seems to be inconsistent... According to Pochhammer symbol, there shouldn't be any negative signs on the RHS... Specifically, if we define

(x)_n=\frac{\Gamma(x+1)}{\Gamma(x-n+1)}.

then according to Mathematica, the consistent RHS is

\frac{1}{k!}(\alpha)_k,. I think someone may have used the mathworld article which only uses one type of Pochhammer symbol.--Lionelbrits 19:40, 30 March 2007 (UTC)

In any case, it seems to me that the use of this Pchh symbol is not relevant here, so I suggest to leave it in the discussion of general Newton's series. PMajer 11:18, 28 April 2007 (UTC)

[edit] Complex values of α

It seems worth enlarging the discussion to the complex values of α. I added a few facts on the binomial coefficients and a sketch of the proof of the elementary results about convergence.PMajer 11:18, 28 April 2007 (UTC)

[edit] Easier

Is it not easier to understand “when to stop” if you write : \frac{\alpha (\alpha-1) (\alpha-2) \cdots (\alpha-(k-1))}{k!}? Anders Ytterström (talk) 12:16, 14 June 2008 (UTC)