Related papers: q-Euler and Genocchi numbers
Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of…
We give a $q$-analogue of $\zeta(6)=\pi^6/945$. Our main results are stated in Theorems 2.1 and 2.2 below.
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
We provide some variations on the Greene-Krammer's identity which involve q-Catalan numbers. Our method reveals a curious analogy between these new identities and some congruences modulo a prime.
We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
In this paper we prove that q-Euler numbers are occured in the coefficients of some stirling type seies for p-adic analytic q-log gamma function
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions.…
By considering Eulerian numbers and ordered Stirling numbers of the second and third kinds over a multiset, we generalize identities of Eulerian numbers and Stirling numbers of the second and third kinds and provide $q$-analogs of these…
In this paper we study that the $q$-Euler numbers and polynomials are analytically continued to $E_q(s)$. A new formula for the Euler's $q$-Zeta function $\zeta_{E,q}(s)$ in terms of nested series of $\zeta_{E,q}(n)$ is derived. Finally we…
In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.
The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of…
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…
By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations.…
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…
Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer's generalized Euler numbers are studied to give certain…
We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials…
The present paper deals with unification of the multiple twisted Euler and Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q = 1. Some earlier results of Ozden's papers in terms of unification of the multiple…
The aim of this paper is to present a general algebraic identity. Applying this identity, we provide several formulas involving the q-binomial coefficients and the q-harmonic numbers. We also recover some known identities including an…
We give a q-analogue of Gauss' divisibility theorem
We give a $q$-analog of middle convolution for linear $q$-difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he examined properties of middle convolution in detail. In this…