scholarly journals A New Class of Hermite-Fubini Polynomials and Its Properties

2019 ◽  
Author(s):  
Waseem Khan ◽  
Nisar K S
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

scholarly journals A Note on Degenerate Hermite-Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan ◽  
Idrees A. Khan ◽  
Nisar K S
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we introduce a new class of degenerate Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of degenerate Hermite-Fubini numbers and polynomials by using generating functions.

scholarly journals A New Class of Laguerre-Based Hermite-Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Nisar K S ◽  
Idrees A. Khan
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we introduce a new class of Laguerre-based Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Laguerre-based Hermite-Fubini numbers and polynomials by using generating functions.

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.

scholarly journals A Note on the Truncated-Exponential Based Apostol-Type Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 538 ◽  
Author(s):  
H. M. Srivastava ◽  
Serkan Araci ◽  
Waseem A. Khan ◽  
Mehmet Acikgöz
Keyword(s):  
Generating Functions ◽  
Bernoulli Polynomials ◽  
New Family ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar Apostol-type polynomials. We also obtain some implicit summation formulas and symmetric identities by using their generating functions. The results, which we have derived here, provide generalizations of the corresponding known formulas including identities involving generalized Hermite-Bernoulli polynomials.

scholarly journals On Generalized Grahaml Numbers

2020 ◽  
pp. 42-57
Author(s):  
Yuksel Soykan
Keyword(s):  
Generating Functions ◽  
Summation Formulas ◽  
Special Cases

In this paper, we introduce the generalized Grahaml sequences and we deal with, in detail, three special cases which we call them Grahaml, Grahaml-Lucas and modified Grahaml sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

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.

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