Abstract
ABSTRACT A polynomial sequence is symmetric, or self-dual, if for all . In this paper, we give the characterization of the exponential symmetric Sheffer sequences with weight sequences, and show that all the symmetric Sheffer sequences with weight , or are in fact constant multiples of the Charlier polynomial sequence, the Meixner polynomial sequence, or the Krawtchouk polynomial sequence, respectively, where are the rising factorials, and are the falling factorials.
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