218 research outputs found
A simpler characterization of Sheffer polynomial
We characterize the Sheffer sequences by a single convolution identity where is a
shift-invariant operator. We then study a generalization of the notion of
Sheffer sequences by removing the requirement that be
shift-invariant. All these solutions can then be interpreted as cocommutative
coalgebras. We also show the connection with generalized translation operators
as introduced by Delsarte. Finally, we apply the same convolution to symmetric
functions where we find that the ``Sheffer'' sequences differ from ordinary
full divided power sequences by only a constant factor
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