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Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤp
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In this paper, a systemic study of some families of q-Euler numbers and polynomials of Norlund type is presented by using the multivariate fermionic p-adic integral on ℤ p.Abstract:
A systemic study of some families of q-Euler numbers and families of polynomials of Norlund type is presented by using the multivariate fermionic p-adic integral on ℤ p . The study of these higher-order q-Euler numbers and polynomials yields an interesting q-analog of identities for Stirling numbers.read more
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A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
Serkan Araci,Mehmet Acikgoz +1 more
Abstract: The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of Bernstein polynomials and Frobenius-Euler numbers and polynomials. To be more precise we summarize our results as follows, we obtain some combinatorial relations between Frobenius-Euler numbers and polynomials. Furthermore, we derive an integral representation of Bernstein polynomials of degree n on Zp . Also we deduce a fermionic p-adic integral representation of product Bernstein polynomials of different degrees n1, n2,...on Zp and show that it can be written with Frobenius-Euler numbers which yields a deeper insight into the effectiveness of this type of generalizations. Our applications possess a number of interesting properties which we state in this paper.
Journal ArticleDOI
Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials
Abdelmejid Bayad,Taekyun Kim +1 more
TL;DR: In this article, the authors give relations involving values of q-Bernoulli, q-Euler, and Bernstein polynomials, and obtain some interesting identities on the qBernoullians.
Journal ArticleDOI
Identities involving Frobenius–Euler polynomials arising from non-linear differential equations
TL;DR: In this article, the authors consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials and derive some new identities between the sums of products of the two classes.
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A Study on the Fermionic -Adic -Integral Representation on ℤ Associated with Weighted -Bernstein and -Genocchi Polynomials
TL;DR: In this paper, the authors considered weighted ǫ-Genocchi numbers and polynomials and investigated some interesting properties of the weighted Ã-Gonzalez numbers related to weighted Ò-Bernstein polynomial by using fermionic à -adic integrals on Ω(ǫ).
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Barnes-type multiple q-zeta functions and q-Euler polynomials
TL;DR: Kim et al. as mentioned in this paper presented a systemic study of some families of multiple q-Euler numbers and polynomials and constructed multiple Q-zeta functions which interpolate multiple q Euler numbers at a negative integer.
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Journal ArticleDOI
q-Euler numbers and polynomials associated with p-adic q-integrals
TL;DR: The main purpose of as discussed by the authors is to present a systemic study of some families of multiple q-Euler numbers and polynomials, using the q-Volkenborn integration on Zp.
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Euler Numbers and Polynomials Associated with Zeta Functions
TL;DR: In this paper, the Euler zeta function and the Hurwitz-type Euler Zeta function are defined by, and they are shown to have the values of Euler numbers or Euler polynomials at negative integers.
Journal ArticleDOI
On a p-adic interpolation function for the Euler numbers and its derivatives
Katsumi Shiratani,Sunao Yamamoto +1 more
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On p-adic interpolating function for q-Euler numbers and its derivatives
TL;DR: In this paper, a two-variable p-adic q -adic q l -function l p, q ( s, t | χ ) for Dirchlet's character χ was studied and proved to be analytic in s and t for s ∈ C p with | s | p p 1 − 1 p − 1 and | t | p ⩽ 1.