Related papers: Some identities on degenerate hyperbolic functions…
In this paper, we give some identities of symmetry for the generalized degenerate Euler polynomials attached to chi which are derived from the symmetric properties for certain fermionic p-adic integrals on Zp.
We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.
We review the teory of the pseudo-iperbolic functions on the basis of an algebraic point of view which employs the Eisenstein group. We frame the teory within the general context of the number decomposition and discuss the importance of…
In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…
In this paper, we give a fermionic p-adic integral representions of Benstein polynomials associated with Euler numbers and polynomials. Finally, we give some interesting identities for the Euler numbers by using the properties of our…
In this paper, hyperbolic k-Fibonacci quaternions are defined. Also, some algebraic properties of hyperbolic k-Fibonacci quaternions which are connected with hyperbolic numbers and k-Fibonacci numbers are investigated. Furthermore,…
We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…
In this paper, obtained some new class of Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities via fractional integrals for the p-hyperbolic convex functions. It is shown that such inequalities are simple consequences of…
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…
The purpose of this paper is to construct p-adic Dedekind sums and Hardy-Berndt type sums. We also construct generating function of the twisted Bernoulli polynomials and functions. Furthermore, we give some discussions on elliptic analogue…
The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of…
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 the former part of this paper, we summarize our previous results on infinite series involving the hyperbolic sine function, especially, with a focus on the hyperbolic sine analogue of Eisenstein series. Those are based on the classical…
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…
The definition for the $p$-adic Hurwitz-type Euler zeta functions has been given by using the fermionic $p$-adic integral on $\mathbb Z_p$. By computing the values of this kind of $p$-adic zeta function at negative integers, we show that it…
Recently, the degenerate harmonic and the degenerate hyperharmonic numbers are introduced respectively as degenerate versions of the harmonic and the hyperharmonic numbers. The aim of this paper is to introduce the degenerate…
By applying the p-adic q-Volkenborn Integrals including the bosonic and the fermionic p-adic integrals on p-adic integers, we define generating functions, attached to the Dirichlet character, for the generalized Apostol-Bernoulli numbers…
Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
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.