Symmetric identities for Carlitz's type twisted q-Genocchi polynomials using twisted q-Genocchi zeta function

2014 ◽  
Vol 8 ◽  
pp. 4405-4412
Author(s):  
J. Y. Kang ◽  
C. S. Ryoo
2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Alejandro Urieles ◽  
William Ramírez ◽  
María José Ortega ◽  
Daniel Bedoya

Abstract The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.


Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 395
Author(s):  
Cheon Ryoo

The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction with ( p , q ) -analogue of tangent numbers and polynomials. We give some new symmetric identities for ( p , q ) -analogue of tangent polynomials by using ( p , q ) -tangent zeta function. Finally, we investigate the distribution and symmetry of the zero of ( p , q ) -analogue of tangent polynomials with numerical methods.


2021 ◽  
Vol 45 (6) ◽  
pp. 859-872
Author(s):  
WASEEM A. KHAN ◽  
◽  
DIVESH SRIVASTAVA

This paper is well designed to set-up some new identities related to generalized Apostol-type Hermite-based-Frobenius-Genocchi polynomials and by applying the generating functions, we derive some implicit summation formulae and symmetric identities. Further a relationship between Array-type polynomials, Apostol-type Bernoulli polynomials and generalized Apostol-type Frobenius-Genocchi polynomials is also established.


Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1967-1977 ◽  
Author(s):  
Waseem Khan ◽  
Divesh Srivastava

The main object of this work is to introduce a new class of the generalized Apostol-type Frobenius-Genocchi polynomials and is to investigate some properties and relations of them. We derive implicit summation formulae and symmetric identities by applying the generating functions. In addition a relation in between Array-type polynomials, Apostol-Bernoulli polynomials and generalized Apostol-type Frobenius-Genocchi polynomials is also given.


Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1670
Author(s):  
Ahyun Kim ◽  
Cheon Seoung Ryoo

In this paper, we study Carlitz’s type higher-order (p,q)-Genocchi polynomials. To be specific, we define Carlitz’s type higher-order (p,q)-Genocchi polynomials and Carlitz’s type higher-order (h,p,q)-Genocchi polynomials. This paper also explores properties including distribution relation and symmetric identities. In addition, we find alternating (p,q)-power sums. We identify symmetric identities using Carlitz’s type higher-order (h,p,q)-Genocchi polynomials and alternating (p,q)-power sums.


2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
J. Y. Kang ◽  
H. Y. Lee ◽  
N. S. Jung ◽  
C. S. Ryoo

Using fermionic -adic invariant integral on , we construct the Barnes' type multiple Genocchi numbers and polynomials. From those numbers and polynomials, we derive the twisted Barnes' type multiple Genocchi numbers and polynomials. Moreover, we will find the Barnes' type multiple Genocchi zeta function.


Sign in / Sign up

Export Citation Format

Share Document