an a-statistical proof of a binomial identity

When waiting for Andrew this morning, I was browsing through the arXived papers of the day and came across this “Simple Statistical Proof of a Binomial Identity” by P. Vellaisamy. The said identity is that, for all s>0,

\sum_{k=0}^n (-1)^k {n \choose k}\dfrac{s}{s+k} = \prod_{k=1}^n \dfrac{k}{k+s}

Nothing wrong with the maths in this paper (except for a minor typo using Exp(1) instead of Exp(s), p.2).  But I am perplexed by the label “statistical” used by the author, as this proof is an entirely analytic argument, based on two different integrations of the same integral. Nothing connected with data or any statistical  technique: this is sheer combinatorics, of the kind one could find in William Feller‘s volume I.

One Response to “an a-statistical proof of a binomial identity”

  1. […] fits almost exactly from the start. This accuracy was already pointed out by William Feller, Section […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.