A New Class of Generalized Polynomials Associated with Hermite and Euler Polynomials

2015 ◽  
Vol 13 (3) ◽  
pp. 913-928 ◽  
Author(s):  
M. A. Pathan ◽  
Waseem A. Khan
Keyword(s):  
Euler Polynomials ◽  
Generalized Polynomials ◽  
New Class

scholarly journals Some New Classes of Generalized Apostol-Euler and Apostol-Genocchi Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
R. Tremblay ◽  
S. Gaboury ◽  
B.-J. Fugère
Keyword(s):  
Addition Theorem ◽  
Euler Polynomials ◽  
Addition Formula ◽  
New Class ◽  
Genocchi Polynomials

The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér (2004) and R. Tremblay, S. Gaboury, B.-J. Fugère, and Tremblay et al. (2011). for both classes.

scholarly journals A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order

2020 ◽  
Vol 13 (3) ◽  
pp. 587-607
Author(s):  
Nestor Gonzales Acala
Keyword(s):  
Hypergeometric Function ◽  
Explicit Formula ◽  
Higher Order ◽  
Gaussian Hypergeometric Function ◽  
Generalized Polynomials ◽  
New Class ◽  
Genocchi Polynomials

Most unifications of the classical or generalized Bernoulli, Euler, and Genocchi polynomials involve unifying any two or all of the three special types of polynomials (see, [1, 4, 9, 18, 19,21, 24–26, 30, 31]). In this paper, we introduce a new class of multiparameter Fubini-type gener-alized polynomials that unifies four families of higher order generalized Apostol-type polynomials such as the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Fubini polynomials. Moreover, we obtain an explicit formula of these unified generalized polynomials in terms of the Gaussian hypergeometric function, and establish several symmetry identities.

scholarly journals Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

2015 ◽  
Vol 55 (1) ◽  
pp. 153-170 ◽  
Author(s):  
M. A. Pathan ◽  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a new class of generalized Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials and derive some implicit summation formulae by applying the generating functions. These results extend some known summations and identities of generalized Hermite-Euler polynomials studied by Dattoli et al, Kurt and Pathan.

scholarly journals Some (p, q)-analogues of Apostol type numbers and polynomials

2019 ◽  
Vol 23 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Mehmet Acikgoz ◽  
Serkan Araci ◽  
Ugur Duran
Keyword(s):  
Generating Functions ◽  
Bernoulli Polynomials ◽  
Euler Polynomials ◽  
New Class

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several old and new identities concerning Apostol–Bernoulli and Apostol–Euler polynomials. Finally, we define the (p, q)-generalization of Stirling polynomials of the second kind of order v, and provide a link between the (p, q)-generalization of Bernoulli polynomials of order v and the (p, q)-generalization of Stirling polynomials of the second kind of order v.

A New Class of Laguerre-Based Poly-Euler and Multi Poly-Euler Polynomials

2016 ◽  
Vol 4 (2) ◽  
pp. 113-120 ◽  
Author(s):  
N. U. Khan ◽  
T. Usman
Keyword(s):  
Euler Polynomials ◽  
New Class

scholarly journals A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 652
Author(s):  
Serkan Araci ◽  
Mumtaz Riyasat ◽  
Shahid Wani ◽  
Subuhi Khan
Keyword(s):  
Generating Function ◽  
Zeta Functions ◽  
Euler Polynomials ◽  
Power Sums ◽  
New Class ◽  
Summation Formulae ◽  
Special Cases ◽  
Hybrid Class

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz–Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations.

A new class of generalized Laguerre–Euler polynomials

2018 ◽  
Vol 113 (2) ◽  
pp. 861-873 ◽  
Author(s):  
Nabiullah Khan ◽  
Talha Usman ◽  
Junesang Choi
Keyword(s):  
Euler Polynomials ◽  
New Class
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