Displaying similar documents to “A generalization of the Bernoulli polynomials.”

On certain generalized q-Appell polynomial expansions

Thomas Ernst (2015)

Annales UMCS, Mathematica

Similarity:

We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...

On certain generalized q-Appell polynomial expansions

Thomas Ernst (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials...

On mth order Bernoulli polynomials of degree m that are Eisenstein

Arnold Adelberg, Michael Filaseta (2002)

Colloquium Mathematicae

Similarity:

This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.

Rota-Baxter operators and Bernoulli polynomials

Vsevolod Gubarev (2021)

Communications in Mathematics

Similarity:

We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.

Fully degenerate poly-Bernoulli numbers and polynomials

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

Open Mathematics

Similarity:

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.