On Apostol-Type Hermite Degenerated Polynomials (original) (raw)
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A new class of degenerate Apostol-type Hermite polynomials and applications
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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
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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.
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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.
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In this article, we give a new generalization of the Apostol Hermite-Genocchi polynomials. Some implicit summation formula and general symmetric identities for these polynomials are derived. Moreover, many important specials cases are obtained. We show that the results given in Serkan et al. [1] and Gaboury and Kurt [5]` are special cases of our results.
Generalized Hermite-based Apostol-Euler Polynomials and Their Properties
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The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynomials with three parameters. We have shown that there is an intimate connection between these polynomials and established their elementary properties. We also established some identities by applying the generating functions and deduce their special cases and applications
On degenerate Apostol-type polynomials and applications
Boletín de la Sociedad Matemática Mexicana
The main object of the current paper is to introduce and investigate a new unified class of the degenerate Apostol-type polynomials. These polynomials are studied by means of the generating function, series definition and are framed within the context of monomiality principle. Several important recurrence relations and explicit representations for the antecedent class of polynomials are derived. As the special cases, the degenerate Apostol-Bernoulli, Euler and Genocchi polynomials are obtained and corresponding results are also proved. A fascinating example is constructed in terms of truncated-exponential polynomials, which gives the applications of these polynomials to produce their hybridized forms.
A Unified Family of Generalized qqq-Hermite Apostol Type Polynomials and its Applications
Communications in Advanced Mathematical Sciences
The intended objective of this paper is to introduce a new class of generalized q-Hermite based Apostol type polynomials by combining the q-Hermite polynomials and a unified family of q-Apostol-type polynomials. The generating function, series definition and several explicit representations for these polynomials are established. The q-Hermite-Apostol Bernoulli, q-Hermite-Apostol Euler and q-Hermite-Apostol Genocchi polynomials are studied as special members of this family and corresponding relations for these polynomials are obtained.
Applying the monomiality principle to the new family of Apostol Hermite Bernoulli-type polynomials
Communications in Applied and Industrial Mathematics Communications in Applied and Industrial Mathematics , 2024
In this article, we introduce a new class of polynomials, known as Apostol Hermite Bernoulli-type polynomials, and explore some of their algebraic properties, including summation formulas and their determinant form. The majority of our results are proven using generating function methods. Additionally, we investigate the monomiality principle related to these polynomials and identify the corresponding derivative and multiplicative operators.
Archivum Mathematicum
One can find in the mathematical literature many recent papers studying the generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, defined by means of generating functions. In this article we clarify the range of parameters in which these definitions are valid and when they provide essentially different families of polynomials. In particular, we show that, up to multiplicative constants, it is enough to take as the "main family" those given by