Abstract. Recently, the q-Euler numbers and polynomials are constructed in [T. Kim, The modified q-Euler numbers and polynomials, Advanced Studies in Contemporary Mathematics, 16(2008), 161-170]. These q-Euler numbers and polynomials contain the interesting properties. In this paper we prove Von-Staudt Clausen’s type theorem related to the q-Euler numbers. That is, we prove that the q-Euler num...

in this paper, a practical review of the adomian decomposition method, to extend the procedure to handle the strongly nonlinear problems under the mixed conditions, is given and the convergence of the algorithm is proved. for this respect, a new and simple way to generate the adomian polynomials, for a general nonlinear function, is proposed. the proposed procedure, provides an explicit formula...

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and polynomials. Furthermore we construct multivariate Hurwitz type zeta function which interpolates the multivariate q-Euler numbers or polynomials at negative ...

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustra...

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric have been studied in the literature with help generating functions their functional equations. In this paper, using (p,q)–Fibonacci (p,q)–Lucas Changhee numbers, we define (p,q)–Fibonacci–Changhee polynomials (p,q)–Lucas–Changhee respectively. We obtain some important identities relations these new...

Motivated by Kurt’s work [Filomat 30 (4) 921-927, 2016], we …rst consider a class of a new generating function for (p; q)-analog of Apostol type polynomials of order including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order . By making use of their generating function, we derive some useful identities. We also introduce (p; q)-analog of Stirling numbers of second kind...

Adopting the definition of excedances of type B due to Brenti, we give a type B analogue of the q-derangement polynomials. The connection between q-derangement polynomials and Eulerian polynomials naturally extends to the type B case. Based on this relation, we derive some basic properties of the q-derangement polynomials of type B, including the generating function formula, the Sturm sequence ...

The present paper deals with the various q-Genocchi numbers and polynomials. We define a new type ofmultiple generalized q-Genocchi numbers and polynomials withweight α andweakweight β by applying the method of p-adic q-integral. We will find a link between their numbers and polynomials with weight α and weak weight β. Also we will obtain the interesting properties of their numbers and polynomi...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...