On the Symmetric Properties of the Multivariate p-Adic Invariant Integral on ℤp Associated with the Twisted Generalized Euler Polynomials of Higher Order

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.

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A note on symmetric properties of the multiple q-Euler zeta functions and higher-order q-Euler polynomials

Applied Mathematical Sciences ◽

10.12988/ams.2014.42117 ◽

2014 ◽

Vol 8 ◽

pp. 1585-1591 ◽

Cited By ~ 1

Author(s):

Dae San Kim ◽

Taekyun Kim ◽

Seog-Hoon Rim ◽

Jong-Jin Seo

Keyword(s):

Zeta Functions ◽

Higher Order ◽

Euler Polynomials ◽

Symmetric Properties

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Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

Abstract and Applied Analysis ◽

10.1155/2009/848943 ◽

2009 ◽

Vol 2009 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Taekyun Kim ◽

Seog-Hoon Rim ◽

Byungje Lee

Keyword(s):

Bernoulli Polynomials ◽

Bernoulli Numbers ◽

Bernoulli Numbers And Polynomials ◽

Power Sums ◽

Invariant Integral ◽

Generalized Bernoulli Polynomials ◽

Symmetric Properties

By the properties ofp-adic invariant integral onℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties ofp-adic invariant integral onℤp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.

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Symmetric properties for generalized Euler polynomials of the second kind

International Journal of Contemporary Mathematical Sciences ◽

10.12988/ijcms.2017.7622 ◽

2017 ◽

Vol 12 ◽

pp. 191-199

Author(s):

Cheon Seoung Ryoo

Keyword(s):

Euler Polynomials ◽

Symmetric Properties

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

Symmetry ◽

10.3390/sym11050645 ◽

2019 ◽

Vol 11 (5) ◽

pp. 645 ◽

Cited By ~ 4

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.

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