The classical umbral calculus: Sheffer sequences

Details The classical umbral calculus: Sheffer sequences The classical umbral calculus: Sheffer sequences

2008-10-20

arxiv.org/abs/0810.3554v1

Mathematics

Combinatorics

Scientific paper

Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax allows us noteworthy computational simplifications and conceptual clarifications in many results involving Sheffer sequences. To give an indication of the effectiveness of the theory, we describe applications to the well-known connection constants problem, to Lagrange inversion formula and to solving some recurrence relations.

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