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Sur une propriété des polynômes de Nörlund

Farid Bencherif (2010)

Actes des rencontres du CIRM

In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.

Symbolic discrepancy and self-similar dynamics

Boris Adamczewski (2004)

Annales de l'Institut Fourier

We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitution. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems.

Symmetric identity for polynomial sequences satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x )

Farid Bencherif, Rachid Boumahdi, Tarek Garici (2021)

Communications in Mathematics

Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x ) with A 0 ( x ) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.

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