Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, Norlund, hypergeometric Bernoulli, and Legendre polynomials. Moreover, we obtain a generalization of Carlitz’s identity for Bernoulli numbers and polynomials to arbitrary symmetric s-Appell polynomials.

Combinatorial identities for Appell polynomials

E. Munarini
2018-01-01

Abstract

Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, Norlund, hypergeometric Bernoulli, and Legendre polynomials. Moreover, we obtain a generalization of Carlitz’s identity for Bernoulli numbers and polynomials to arbitrary symmetric s-Appell polynomials.
2018
Combinatorial sums, umbral calculus, orthogonal polynomials, formal series, generating functions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1079615
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