Symbolization of generating functions; an application of the MullinRota theory of binomial enumeration
We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the MullinRota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.
generating function binomial enumeration symbolic sum formula shift-invariant operator delta operator bell number genocchi number euler number euler polynomial eulerian fraction bernoulli number bernoulli polynomial