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Fractions de Bernoulli-Carlitz et opérateurs q -Zeta

Frédéric Chapoton (2010)

Journal de Théorie des Nombres de Bordeaux

On introduit une déformation des séries de Dirichlet d’une variable complexe s , sous la forme d’un opérateur pour chaque nombre complexe s , agissant sur les séries formelles sans terme constant en une variable q . On montre que les fractions de Bernoulli-Carlitz sont les images de certains polynômes en q par les opérateurs associés à la fonction ζ de Riemann aux entiers négatifs.

Fully degenerate poly-Bernoulli numbers and polynomials

Taekyun Kim, Dae San Kim, Jong-Jin Seo (2016)

Open Mathematics

In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.

Generalized poly-Cauchy polynomials and their interpolating functions

Takao Komatsu, Florian Luca, Claudio de J. Pita Ruiz V. (2014)

Colloquium Mathematicae

We give a generalization of poly-Cauchy polynomials and investigate their arithmetical and combinatorial properties. We also study the zeta functions which interpolate the generalized poly-Cauchy polynomials.

Identities arising from higher-order Daehee polynomial bases

Dae San Kim, Taekyun Kim (2015)

Open Mathematics

Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.

Kummer congruences for expressions involving generalized Bernoulli polynomials

Glenn J. Fox (2002)

Journal de théorie des nombres de Bordeaux

We illustrate how a particular expression, involving the generalized Bernoulli polynomials, satisfies systems of congruence relations if and only if a similar expression, involving the generalized Bernoulli numbers, satisfies the same congruence relations. These congruence relations include the Kummer congruences, and recent extensions of the Kummer congruences provided by Gunaratne.

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