Related papers: Barnes' multiple Bernoulli and poly-Bernoulli mixe…
The Barnes multiple zeta function is useful to study in the number theory and Knot thoey and Mathematical Physics. In this paper we consider q-extension of Barnes type multiple zeta function and we also construct the q-extension of Euler…
In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous…
In this paper, some formulae for Genoochi polynomials of higher order are derived using the fact that sets of Bernoulli and Euler polynomials of higher order form basis for the polynomial space.
In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a…
In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.
A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell 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…
Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new…
In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.
The objective of this paper is to derive some interesting properties of Genocchi, Euler and Bernstein polynomials by means of the orthogonality of Hermite polynomials.
We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…
The Poupard polynomials are polynomials in one variable with integer coefficients, with some close relationship to Bernoulli and tangent numbers. They also have a combinatorial interpretation. We prove that every Poupard polynomial has all…
In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the…
We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.
Recently we introduced a new class of relations for Bernoulli symmetric polynomials. This manuscript shows that these relations are valid for arbitrary homogeneous symmetric polynomial. Analysis of these relations leads to the discovery of…
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…
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…