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
Keyword(s):  
Zeta Function ◽  
Genocchi Polynomials ◽  
Symmetric Identities

scholarly journals Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Alejandro Urieles ◽  
William Ramírez ◽  
María José Ortega ◽  
Daniel Bedoya
Keyword(s):  
Fourier Series ◽  
Integral Representation ◽  
Zeta Function ◽  
Fourier Expansion ◽  
Series Representation ◽  
Hurwitz Zeta Function ◽  
Euler Polynomials ◽  
Genocchi Polynomials ◽  
Lerch Zeta Function ◽  
Rational Arguments

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.

scholarly journals Symmetric Identities for (P,Q)-Analogue of Tangent Zeta Function

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 395
Author(s):  
Cheon Ryoo
Keyword(s):  
Numerical Methods ◽  
Zeta Function ◽  
Explicit Formulas ◽  
Symmetric Identities

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.

scholarly journals Certain Properties of Apostol-Type Hermite-Based- Frobenius-Genocchi Polynomials

2021 ◽  
Vol 45 (6) ◽  
pp. 859-872
Author(s):  
WASEEM A. KHAN ◽  
◽  
DIVESH SRIVASTAVA
Keyword(s):  
Generating Functions ◽  
Bernoulli Polynomials ◽  
Array Type ◽  
Genocchi Polynomials ◽  
Summation Formulae ◽  
Symmetric Identities ◽  
Set Up

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.

scholarly journals On the generalized Apostol-type Frobenius-Genocchi polynomials

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1967-1977 ◽  
Author(s):  
Waseem Khan ◽  
Divesh Srivastava
Keyword(s):  
Generating Functions ◽  
Bernoulli Polynomials ◽  
Array Type ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae ◽  
Symmetric Identities

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.

scholarly journals Symmetric Identities for Carlitz’s Type Higher-Order (p,q)-Genocchi Polynomials

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1670
Author(s):  
Ahyun Kim ◽  
Cheon Seoung Ryoo
Keyword(s):  
Higher Order ◽  
Power Sums ◽  
Genocchi Polynomials ◽  
Symmetric Identities

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.

scholarly journals On the Barnes' Type Related to Multiple Genocchi Polynomials on

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
J. Y. Kang ◽  
H. Y. Lee ◽  
N. S. Jung ◽  
C. S. Ryoo
Keyword(s):  
Zeta Function ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
Invariant Integral

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.

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