A new extension of q-Euler numbers and polynomials related to their interpolation functions
نویسندگان
چکیده
In this work, by using a p-adic q-Volkenborn integral, we construct a new approach to generating functions of the (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ . By applying the Mellin transformation and a derivative operator to these functions, we define (h, q)-extensions of zeta functions and l-functions, which interpolate (h, q)-extensions of Euler numbers at negative integers. c © 2007 Elsevier Ltd. All rights reserved.
منابع مشابه
Note on q-Extensions of Euler Numbers and Polynomials of Higher Order
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...
متن کاملOn Multiple Interpolation Functions of the q-Genocchi Polynomials
Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler, Genocchi numbers and their interpolation functions, “Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105– 112, 2009.”, Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In ...
متن کاملOn a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and its derivative
Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...
متن کاملOn the p-Adic Interpolation Functions of the Generalized Twisted (h, q)-Euler Numbers
Recently, Cangul et al. [I.N. Cangul, H. Ozden and Y. Simsek, Generating functions of the (h, q) extension of twisted Euler polynomials and numbers, Acta Math. Hungar. 120(3) (2008), 281-299] constructed new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. They also constructed the partially twisted (h, q)-zeta function. They suggeste...
متن کاملResearch Article Some Relationships between the Analogs of Euler Numbers and Polynomials
We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet l-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distrib...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Appl. Math. Lett.
دوره 21 شماره
صفحات -
تاریخ انتشار 2008