On Apostol-Type Hermite Degenerated Polynomials (original) (raw)
A new class of degenerate Apostol-type Hermite polynomials and applications
A new class of degenerate Apostol-type Hermite polynomials and applications, 2022
In this article, a new class of the degenerate Apostol-type Hermite polynomials is introduced. Certain algebraic and differential properties of there polynomials are derived. Most of the results are proved by using generating function methods.
The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order α and level m in the variable x. Here the degenerate polynomials are a natural extension of the classic polynomials. In more detail, we derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. Most of the results are proved by using generating function methods.
A New Class of Generalized Hermite Based Apostol Type Polynomials
2021
In recent years, various mathematicians (such as Ernst, U. Duran) introduced an extension of Apostol Type polynomials of order α. Recently, W. A. Khan introduced a new class of qHermite based Apostol type polynomials. Motivated by their research, this article introduces a new class of (p,q)analogue of Hermite based Apostol type polynomials of order α and investigate its characteristics.In particular, it establishes the generating function, series expression and explicit relation for these polynomials. It also explores the relationship between generalized Bernoulli, Euler and Genocchi polynomials.
A new generalization of Apostol type Hermite-Genocchi polynomials and its applications
SpringerPlus, 2016
By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite-Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679-695, 2015a) and Hermite-Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite-Genocchi polynomials defined in this paper.
WSEAS transactions on mathematics, 2022
The main objective of this work is to deduce some interesting algebraic relationships that connect the degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials and other families of polynomials such as the generalized Bernoulli polynomials of level m and the Genocchi polynomials. Futher, find new recurrence formulas for these three families of polynomials to study.
Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials
Journal of Mathematical Analysis and Applications, 2005
The main object of this paper is to give analogous definitions of Apostol type (see [T.M. Apostol, On the Lerch Zeta function, Pacific J. Math. 1 (1951) 161-167] and [H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000) 77-84]) for the so-called Apostol-Bernoulli numbers and polynomials of higher order. We establish their elementary properties, derive several explicit representations for them in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) Zeta function, and deduce their special cases and applications which are shown here to lead to the corresponding results for the classical Bernoulli numbers and polynomials of higher order.
arXiv: Classical Analysis and ODEs, 2019
The aim of this paper is to construct generating functions for new families of special polynomials including the Appel polynomials, the Hermite-Kampe de Feriet polynomials, the Milne-Thomson type polynomials, parametric kinds of Apostol type numbers and polynomials. Using Euler's formula, relations among special functions, Hermite-type polynomials, the Chebyshev polynomials and the Dickson polynomials are given. Using generating functions and their functional equations, various formulas and identities are given. With help of computational formula for new families of special polynomials, some of their numerical values are given. Using hypegeometric series, trigonometric functions and the Euler's formula, some applications related to Hermite-type polynomials are presented. Finally, further remarks, observations and comments about generating functions for new families of special polynomials are given.
A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications
Symmetry, 2018
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.
Certain Laguerre-based Generalized Apostol Type Polynomials
Tamkang Journal of Mathematics
A variety of polynomials, their extensions and variants have been extensively investigated, due mainly to their potential applications in diverse research areas. In this paper, we aim to introduce Laguerre-based generalized Apostol type polynomials and investigate some properties and identities involving them. Among them, some differential-recursive relations for the Hermite-Laguerre polynomials, which are expressed in terms of generalized Apostol type numbers and the Laguerre-based generalized Apostol type polynomials, an implicit summation formula and addition-symmetry identities for the Laguerre-based generalized Apostol type polynomials are presented. The results presented here, being very general, are pointed out to reduce to yield some known or new formulas and identities for relatively simple polynomials and numbers.
A new generalization of Apostol-type Laguerre–Genocchi polynomials
Comptes Rendus Mathematique, 2017
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.