scholarly journals A New Class of Degenerate Hermite Poly-Genocchi Polynomials

2018 ◽  
Author(s):  
Waseem A. Khan ◽  
K.S. Nisar
Keyword(s):  
Generating Functions ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
General Symmetry ◽  
Bernoulli Numbers And Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

In this article, authors introduce a new class of degenerate Hermite poly-Genocchi polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of degenerate Hermite poly-Bernoulli numbers and polynomials studied by Khan [8].

scholarly journals Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials

2017 ◽  
Vol 58 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Waseem A. Khan ◽  
M. Ghayasuddin ◽  
M. Shadab
Keyword(s):  
Generating Functions ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
General Symmetry ◽  
Bernoulli Numbers And Polynomials ◽  
New Class ◽  
Summation Formulae

Abstract In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.

scholarly journals A New Class of Laguerre-based Generalized Apostol Polynomials

2016 ◽  
Vol 57 (1) ◽  
pp. 67-89 ◽  
Author(s):  
N.U. Khan ◽  
T. Usman
Keyword(s):  
Generating Functions ◽  
General Symmetry ◽  
Genocchi Numbers ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

scholarly journals Generalized Tepper’s Identity and Its Application

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 243
Author(s):  
Dmitry Kruchinin ◽  
Vladimir Kruchinin ◽  
Yilmaz Simsek
Keyword(s):  
Number Theory ◽  
Generating Functions ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Combinatorial Analysis ◽  
Euler Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Euler Numbers And Polynomials

The aim of this paper is to study the Tepper identity, which is very important in number theory and combinatorial analysis. Using generating functions and compositions of generating functions, we derive many identities and relations associated with the Bernoulli numbers and polynomials, the Euler numbers and polynomials, and the Stirling numbers. Moreover, we give applications related to the Tepper identity and these numbers and polynomials.

scholarly journals Identities and relations for Fubini type numbers and polynomials via generating functions and p-adic integral approach

2019 ◽  
Vol 106 (120) ◽  
pp. 113-123
Author(s):  
Neslihan Kilar ◽  
Yilmaz Simsek
Keyword(s):  
Functional Equation ◽  
Generating Functions ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Combinatorial Analysis ◽  
Integral Approach ◽  
Euler Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Array Polynomials ◽  
Euler Numbers And Polynomials

The Fubini type polynomials have many application not only especially in combinatorial analysis, but also other branches of mathematics, in engineering and related areas. Therefore, by using the p-adic integrals method and functional equation of the generating functions for Fubini type polynomials and numbers, we derive various different new identities, relations and formulas including well-known numbers and polynomials such as the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers of the second kind, the ?-array polynomials and the Lah numbers.

scholarly journals Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Series Representation ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Eulerian Polynomials ◽  
New Class ◽  
Genocchi Polynomials

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

scholarly journals A Parametric Kind of Fubini Polynomials of a Complex Variable

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 643
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Cheon Seoung Ryoo
Keyword(s):  
Complex Variable ◽  
Generating Functions ◽  
Stirling Numbers ◽  
Genocchi Polynomials ◽  
Summation Formulae ◽  
Analytical Properties

In this paper, we propose a parametric kind of Fubini polynomials by defining the two specific generating functions. We also investigate some analytical properties (for example, summation formulae, differential formulae and relationships with other well-known polynomials and numbers) for our introduced polynomials in a systematic way. Furthermore, we consider some relationships for parametric kind of Fubini polynomials associated with Bernoulli, Euler, and Genocchi polynomials and Stirling numbers of the second kind.

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 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 Some Properties of $Q$-Hermite Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulas

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers.  Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

scholarly journals On the three families of extended Laguerre-based Apostol-type polynomials

2021 ◽  
Vol 40 (2) ◽  
pp. 313-334
Author(s):  
M. A. Pathan ◽  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Hermite Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae ◽  
Symmetric Identities

In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite and Bell-Hermite polynomials and to find new representations. We derive some implicit summation formulae and symmetric identities for these families of special functions by applying the generating functions.

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