Sur une propriété des polynômes de Nörlund
In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.
In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.
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.
Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying with 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.