Some symmetric identities for higher-order q-Euler polynomials under S_5 arising from fermionic p-adic q-integral on Zp

2015 ◽  
Vol 9 ◽  
pp. 1563-1570
Author(s):  
T. Kim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Symmetric Identities

scholarly journals Some symmetric identities for the higher-order q-Euler polynomials related to symmetry group S3 arising from p-adic q-fermionic integrals on Zp

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1717-1721 ◽  
Author(s):  
Dae Kim ◽  
Taekyun Kim
Keyword(s):  
Symmetry Group ◽  
Higher Order ◽  
Euler Polynomials ◽  
Symmetric Identities

The purpose of this paper is to give some new symmetric identities for the higher-order q-Euler polynomials of the first kind related to symmetry group S3 arising from p-adic q-fermionic integrals on Zp.

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.

scholarly journals Symmetric Properties for Dirichlet-Type Multiple (p,q)-L-Function

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 95
Author(s):  
Kyung-Won Hwang ◽  
Ravi P. Agarwal ◽  
Cheon Seoung Ryoo
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Dirichlet Type ◽  
Euler Numbers And Polynomials ◽  
Symmetric Identities ◽  
Symmetric Properties

The main aim of this article is to investigate some interesting symmetric identities for the Dirichlet-type multiple (p,q)-L function. We use this function to examine the symmetry of the generalized higher-order (p,q)-Euler polynomials related to χ. First, the generalized higher-order (p,q)-Euler numbers and polynomials related to χ are defined. We also give a few new symmetric properties for the Dirichlet-type multiple (p,q)-L-function and generalized higher-order (p,q)-Euler polynomials related to χ.

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 A note on the higher-order Frobenius-Euler polynomials and Sheffer sequences

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim ◽  
Sang-Hun Lee ◽  
Seog-Hoon Rim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Sheffer Sequences
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