Talk:Binomial type

A funny sum

Anyone ever see something that looks like this:

$\sum _{k=0}^n(\genfrac{}{}{0ex}{}{n}{k})y^k\frac{1}{k!}\frac{d^k}{d{x}^k}f(x)$

Any identities, relations,etc. for such a thing? Does it have a name? Its painfully suggestive of something but I can't put my finger on it ... linas 04:30, 19 August 2005 (UTC)

Those are called Appel sequences. Like sequences of binomial type, they're a special case of Sheffer sequences. Michael Hardy 18:29, 8 May 2006 (UTC)

i dont get it, whats the definition?