Related papers: On Multi Poly-Bernoulli Polynomials
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.
In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials.…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.
We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few expressions of these numbers.
In this paper, we consstruct a new extended q-Bernoulli numbers and poly nomials. From these numbers, we derive the multiple zeta functions and give some relations between multiple Bernoulli numbers and multiple zeta functions.
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…
We prove sum formulas for double polylogarithms of Hurwitz type, that is, involving a shifting parameter $b$ in the denominator. These formulas especially imply well-known sum formulas for double zeta values, and sum formulas for double…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various…
In this paper we obtain several new identities for Bernoulli and Euler polynomials; some of them extend Miki's and Matiyasevich's identities. Our new method involves differences and derivatives of polynomials.
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
Recently, the higher-order Carlitz's q-Bernoulli polynomials are represented as q-Volkenborn integral on Zp by Kim. A question was asked in [13] as to finding the extended formulaeof symmetries for Bernoulli polynomials which are related to…
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
A symbolic method is used to establish some properties of the Bernoulli-Barnes polynomials.
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In…