scholarly journals Certain results of hybrid families of special polynomials associated with appell sequences

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3833-3844 ◽  
Author(s):  
Ghazala Yasmin ◽  
Abdulghani Muhyi
Keyword(s):  
Generating Functions ◽  
Mixed Type ◽  
Bernoulli Polynomials ◽  
Operational Method ◽  
Appell Polynomials ◽  
Special Polynomials ◽  
Appell Sequences

In this article, the Legendre-Gould-Hopper polynomials are combined with Appell sequences to introduce certain mixed type special polynomials by using operational method. The generating functions, determinant definitions and certain other properties of Legendre-Gould-Hopper based Appell polynomials are derived. Operational rules providing connections between these formulae and known special polynomials are established. The 2-variable Hermite Kamp? de F?riet based Bernoulli polynomials are considered as an member of Legendre-Gould-Hopper based Appell family and certain results for this member are also obtained.

scholarly journals A Note on q -Fubini-Appell Polynomials and Related Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdulghani Muhyi ◽  
Serkan Araci
Keyword(s):  
Present Article ◽  
Generating Functions ◽  
Appell Polynomials ◽  
New Class ◽  
Special Polynomials ◽  
Series Representations ◽  
Polynomial Family

The present article is aimed at introducing and investigating a new class of q -hybrid special polynomials, namely, q -Fubini-Appell polynomials. The generating functions, series representations, and certain other significant relations and identities of this class are established. Some members of q -Fubini-Appell polynomial family are investigated, and some properties of these members are obtained. Further, the class of 3-variable q -Fubini-Appell polynomials is also introduced, and some formulae related to this class are obtained. In addition, the determinant representations for these classes are established.

scholarly journals A Numerical Computation of Zeros of q-Generalized Tangent-Appell Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 383
Author(s):  
Ghazala Yasmin ◽  
Cheon Seoung Ryoo ◽  
Hibah Islahi
Keyword(s):  
Numerical Computation ◽  
Generating Functions ◽  
Graphical Representation ◽  
Appell Polynomials ◽  
New Class ◽  
Special Polynomials

The intended objective of this study is to define and investigate a new class of q-generalized tangent-based Appell polynomials by combining the families of 2-variable q-generalized tangent polynomials and q-Appell polynomials. The investigation includes derivations of generating functions, series definitions, and several important properties and identities of the hybrid q-special polynomials. Further, the analogous study for the members of this q-hybrid family are illustrated. The graphical representation of its members is shown, and the distributions of zeros are displayed.

scholarly journals Generalizations of the Bernoulli and Appell polynomials

2004 ◽  
Vol 2004 (7) ◽  
pp. 613-623 ◽  
Author(s):  
Gabriella Bretti ◽  
Pierpaolo Natalini ◽  
Paolo E. Ricci
Keyword(s):  
Differential Equations ◽  
Generating Functions ◽  
Bernoulli Polynomials ◽  
Factorization Method ◽  
Bernoulli Numbers ◽  
Appell Polynomials

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.

scholarly journals A Note on the Degenerate Type of Complex Appell Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1339 ◽  
Author(s):  
Dojin Kim
Keyword(s):  
Imaginary Part ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
The Real ◽  
General Properties ◽  
Appell Sequences ◽  
Real Value ◽  
Degenerate Type

In this paper, complex Appell polynomials and their degenerate-type polynomials are considered as an extension of real-valued polynomials. By treating the real value part and imaginary part separately, we obtained useful identities and general properties by convolution of sequences. To justify the obtained results, we show several examples based on famous Appell sequences such as Euler polynomials and Bernoulli polynomials. Further, we show that the degenerate types of the complex Appell polynomials are represented in terms of the Stirling numbers of the first kind.

scholarly journals Legendre-Gould Hopper Based Sheffer Polynomials: Properties and Applications

2020 ◽  
Author(s):  
Ghazala Yasmin ◽  
Abdulghani Muhyi
Keyword(s):  
Differential Equations ◽  
Generating Functions ◽  
Mixed Type ◽  
Integral Representations ◽  
Special Polynomials ◽  
Sheffer Sequences ◽  
Sheffer Polynomials

In this article, the Legendre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Generating functions, differential equations and certain other properties of Legendre-Gould Hopper based Sheffer polynomials are derived. Further, operational and integral representations providing connections between these polynomials and known special polynomials are established. Certain identities and results for some members of these new mixed polynomials are also obtained. Finally, the determinantal definitions of Legendre-Gould Hopper based Sheffer polynomials are also given.

On generating functions for the special polynomials

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Yilmaz Simsek
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Special Polynomials ◽  
New Family ◽  
Bernoulli Polynomials And Numbers ◽  
Computation Algorithm ◽  
Generalized Stirling Numbers

The aim of this paper is to investigate and give a new family of Apell type polynomials, which are related to the Euler, Frobenius-Euler and Apostol-Bernoulli polynomials and numbers and also the generalized Stirling numbers of the second kind etc. The results presented in this paper are based upon the theory of the generating functions. By using functional equations of these generating functions, we drive some identities and relations for these numbers and polynomials. Moreover, we give a computation algorithm these numbers.

scholarly journals Some recurrence formulas for the q-Bernoulli and q-Euler polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 663-669
Author(s):  
Paçin Dere
Keyword(s):  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Umbral Calculus ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Derivative Operator ◽  
Important Place ◽  
Quantum Calculus ◽  
Recurrence Formulas ◽  
Special Polynomials

The recurrence relations have a very important place for the special polynomials such as q-Appell polynomials. In this paper, we give some recurrence formulas that allow us a better understanding of q-Appell polynomials. We investigate the q-Bernoulli polynomials and q-Euler polynomials, which are q-Appell polynomials, and we obtain their recurrence formulas by using the methods of the q-umbral calculus and the quantum calculus. Our methods include some operators which are quite handy for obtaining relations for the q-Appell polynomials. Especially, some applications of q-derivative operator are used in this work.

Fractional calculus and generalized forms of special polynomials associated with Appell sequences

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Subuhi Khan ◽  
Shahid Ahmad Wani
Keyword(s):  
Fractional Calculus ◽  
Generating Function ◽  
Recurrence Relations ◽  
Summation Formula ◽  
Integral Transforms ◽  
Operational Definition ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Special Polynomials ◽  
Appell Sequences

Abstract In this article, an operational definition, generating function, explicit summation formula, determinant definition and recurrence relations of the generalized families of Hermite–Appell polynomials are derived by using integral transforms and some known operational rules. An analogous study of these results is also carried out for the generalized forms of the Hermite–Bernoulli and Hermite–Euler polynomials.

Identities related to special polynomials and combinatorial numbers

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Special Polynomials ◽  
Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

Sign in / Sign up

Export Citation Format

Share Document