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

被引：3

作者：

Hwang, Kyung-Won ^{[1
]}

Ryoo, Cheon Seoung ^{[2
]}

机构：

[1] Dong A Univ, Dept Math, Busan 604714, South Korea

[2] Hannam Univ, Dept Math, Daejeon 34430, South Korea

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 05期

关键词：

Euler numbers and polynomials; q-Euler numbers and polynomials; Hurwitz-Euler eta function; multiple Hurwitz-Euler eta function; higher order q-Euler numbers and polynomials; (p; q)-Euler numbers and polynomials of higher order; symmetric identities; symmetry of the zero; POLYNOMIALS; BERNOULLI; EULER;

D O I：

10.3390/sym11050645

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：14

共 20 条

[1]

Agarwal R.P., 2018, J COMPUT ANAL APPL, V24, P1439

[2]

Andrews G.E., 1999, Encycl. Math. Appl., V71

[3]

Araci S, 2016, J INEQUAL APPL, DOI 10.1186/s13660-016-1240-8

[4] EXPANSIONS OF Q-BERNOULLI NUMBERS [J].