scholarly journals On the Higher-Orderq-Euler Numbers and Polynomials with Weightα

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
K.-W. Hwang ◽  
D. V. Dolgy ◽  
T. Kim ◽  
S. H. Lee
Keyword(s):  
Higher Order ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials

The main purpose of this paper is to present a systemic study of some families of higher-orderq-Euler numbers and polynomials with weightα. In particular, by using the fermionicp-adicq-integral onℤp, we give a new concept ofq-Euler numbers and polynomials with weightα.

scholarly journals Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 645 ◽  
Author(s):  
Kyung-Won Hwang ◽  
Cheon Seoung Ryoo
Keyword(s):  
Higher Order ◽  
Complex Field ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Symmetric Identities ◽  
Symmetric Properties

The main purpose of this paper is to find some interesting symmetric identities for the ( p , q ) -Hurwitz-Euler eta function in a complex field. Firstly, we define the multiple ( p , q ) -Hurwitz-Euler eta function by generalizing the Carlitz’s form ( p , q ) -Euler numbers and polynomials. We find some formulas and properties involved in Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order. We find new symmetric identities for multiple ( p , q ) -Hurwitz-Euler eta functions. We also obtain symmetric identities for Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order by using symmetry about multiple ( p , q ) -Hurwitz-Euler eta functions. Finally, we study the distribution and symmetric properties of the zero of Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order.

scholarly journals Multivariate Interpolation Functions of Higher-Orderq-Euler Numbers and Their Applications

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Hacer Ozden ◽  
Ismail Naci Cangul ◽  
Yilmaz Simsek
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Higher Order ◽  
Multivariate Interpolation ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Sums Of Products ◽  
Interpolation Functions

The aim of this paper, firstly, is to construct generating functions ofq-Euler numbers and polynomials of higher order by applying the fermionicp-adicq-Volkenborn integral, secondly, to define multivariateq-Euler zeta function (Barnes-type Hurwitzq-Euler zeta function) andl-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitzq-Euler zeta function and multivariateq-Eulerl-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.

scholarly journals On the Symmetric Properties of Higher-Order Twisted -Euler Numbers and Polynomials

2010 ◽  
Vol 2010 (1) ◽  
pp. 765259 ◽  
Author(s):  
Eun-Jung Moon ◽  
Seog-Hoon Rim ◽  
Jeong-Hee Jin ◽  
Sun-Jung Lee
Keyword(s):  
Higher Order ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Symmetric Properties

Modified Apostol-Euler numbers and polynomials of higher order

2018 ◽  
Vol 11 (4) ◽  
pp. 53-66
Author(s):  
Maged G. Bin-Saad ◽  
Ali Z. Bin-Alhag
Keyword(s):  
Higher Order ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials

scholarly journals ON THE EXTENDED q-EULER NUMBERS AND POLYNOMIALS OF HIGHER-ORDER WITH WEIGHT

2012 ◽  
Vol 34 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Hyun-Mee Kim ◽  
Jong-Sung Choi ◽  
Tae-Kyun Kim
Keyword(s):  
Higher Order ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials

scholarly journals Symmetric Identities for Carlitz-Type Higher-Order Degenerate (p,q)-Euler Numbers and Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1432
Author(s):  
Kyung-Won Hwang ◽  
Cheon Seoung Ryoo
Keyword(s):  
Higher Order ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Order Degenerate ◽  
Symmetric Identities

The main goal of this paper is to investigate some interesting symmetric identities for Carlitz-type higher-order degenerate ( p , q ) -Euler numbers, and polynomials. At first, the Carlitz-type higher-order degenerate ( p , q ) -Euler numbers and polynomials are defined. We give few new symmetric identities for Carlitz-type higher-order degenerate ( p , q ) -Euler numbers and polynomials.

scholarly journals Some Properties for Multiple Twisted (p, q)-L-Function and Carlitz’s Type Higher-Order Twisted (p, q)-Euler Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1205 ◽  
Author(s):  
Kyung-Won Hwang ◽  
Cheon Seoung Ryoo
Keyword(s):  
Generating Functions ◽  
Higher Order ◽  
Integral Representations ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Mellin Transformation ◽  
Euler Numbers And Polynomials ◽  
Symmetric Identities ◽  
Positive Integers ◽  
Symmetric Property

The main goal of this paper is to study some interesting identities for the multiple twisted ( p , q ) -L-function in a complex field. First, we construct new generating functions of the new Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. By applying the Mellin transformation to these generating functions, we obtain integral representations of the multiple twisted ( p , q ) -Euler zeta function and multiple twisted ( p , q ) -L-function, which interpolate the Carlitz-type higher order twisted ( p , q ) -Euler numbers and Carlitz-type higher order twisted ( p , q ) -Euler polynomials at non-positive integers, respectively. Second, we get some explicit formulas and properties, which are related to Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. Third, we give some new symmetric identities for the multiple twisted ( p , q ) -L-function. Furthermore, we also obtain symmetric identities for Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials by using the symmetric property for the multiple twisted ( p , q ) -L-function.

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