Abstract
In this article, we introduce some properties of higher-order-twisted q-Euler numbers and polynomials with weight α, and we observe some properties of higher-order-twisted q-Euler numbers and polynomials with weight α for several cases. In particular, by using the the fermionic p-adic q-integral on ℤ p , we give a new concept of twisted q-Euler numbers and polynomials with weight α. 2000 Mathematics Subject Classification: 11B68; 11S40; 11S80.
Highlights
When one speaks of q-extension, q can be regarded as an indeterminate, a complex number q Î C, or p-adic number q Î Cp; it is always clear from context
The main purpose of this article is to present a systemic study of some families of higherorder-twisted q-Euler numbers and polynomials with weight a
Higher-order-twisted q-Euler numbers and polynomials with weight a For h Î Z, a, k Î N, w Î Tp and n Î Z+, let us consider the expansion of higherorder-twisted q-Euler polynomials with weight a as follows: E,w(h, k|x)
Summary
Let C(Zp) be the space of continuous functions on Zp. For f Î C(Zp), Kim defined the fermionic p-adic q-integral on Zp as follows (see [6,7]): I−q(f ) = X = 0, En(0) = En are called the nth Euler numbers (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14]). For a Î N and w Î Tp, the twisted q-Euler numbers with weight a are defined by
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