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A funny sum

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Anyone ever see something that looks like this:

\sum _{k=0}^{n}{n \choose k}y^{k}{\frac {1}{k!}}{\frac {d^{k}}{dx^{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)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2005-08-19T04:30:00.000Z","author":"Linas","type":"comment","level":1,"id":"c-Linas-2005-08-19T04:30:00.000Z-A_funny_sum","replies":["c-Michael_Hardy-2006-05-08T18:29:00.000Z-Linas-2005-08-19T04:30:00.000Z"]}}-->

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)[reply]__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2006-05-08T18:29:00.000Z","author":"Michael Hardy","type":"comment","level":2,"id":"c-Michael_Hardy-2006-05-08T18:29:00.000Z-Linas-2005-08-19T04:30:00.000Z","replies":[]}}-->