The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér 2004 and R...

Copyright q 2010 Lee-Chae Jang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate several arithmetic properties of h, q-Genocchi polynomials and numbers of higher order.

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rationalnumbers, the complex number field, and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p p−vp p 1/p. When one talks about q-extension, q is variously considered as an i...

Abstract In this paper, we solve the fractional order stiff system using shifted Genocchi polynomials operational matrix. Different than well known polynomials, shift interval from [0, 1] to [1, 2] and name it as polynomials. Using nice properties of which inherit classical matrix derivative will be derived. Collocation scheme are used together with some system. From numerical examples, is obvi...

The aim of this paper is to give generating functions and to prove various properties for some new families of special polynomials and numbers. Several interesting properties of such families and their connections with other polynomials and numbers of the Bernoulli, Euler, Apostol-Bernoulli, ApostolEuler, Genocchi and Fibonacci type are presented. Furthermore, the Fibonacci type polynomials of ...

In this study, we introduce modified degenerate Changhee–Genocchi polynomials of the second kind, and analyze some properties by providing several relations applications. We first attain diverse formulas covering addition formulas, recurrence rules, implicit summation with earlier in literature. By using their generating function, derive new relations, including Stirling numbers kinds. Moreover...

Parameters a, b, c, and α are introduced to form the Bernoulli-type, Euler-type Genocchi-type polynomilas where is order of polynomial a positive integer. Ana- lytic methods used here obtain Fourier series for these polynomials.