scholarly journals Certain Results for the Twice-Iterated 2D q-Appell Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1307 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ghazala Yasmin ◽  
Abdulghani Muhyi ◽  
Serkan Araci
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Subject Matter ◽  
Mixed Type ◽  
Recurrence Relations ◽  
Appell Polynomials ◽  
Function Series ◽  
Potential Applications ◽  
The Subject ◽  
Polynomial Class

In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated.

scholarly journals Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 258 ◽  
Author(s):  
Subuhi Khan ◽  
Tabinda Nahid
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Computer Experiment ◽  
Appell Polynomials ◽  
Distribution Of Zeros ◽  
Hybrid Form ◽  
Special Polynomials

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

scholarly journals Certain Results of q -Sheffer–Appell Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 159 ◽  
Author(s):  
Ghazala Yasmin ◽  
Abdulghani Muhyi ◽  
Serkan Araci
Keyword(s):  
Generating Function ◽  
Appell Polynomials ◽  
Function Series

In this paper, the class of q -Sheffer–Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of q -Sheffer–Appell polynomials are investigated and some properties of these members are derived. In addition, the class of 2D q -Sheffer–Appell polynomials is introduced. Further, the graphs of some members of q -Sheffer–Appell polynomials and 2D q -Sheffer–Appell polynomials are plotted for different values of indices by using Matlab.

scholarly journals General-Appell Polynomials within the Context of Monomiality Principle

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Subuhi Khan ◽  
Nusrat Raza
Keyword(s):  
Differential Equation ◽  
Generating Function ◽  
General Class ◽  
Recurrence Relations ◽  
Appell Polynomials ◽  
Special Polynomials ◽  
New Family ◽  
Special Polynomial

A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases.

scholarly journals A class of big (p,q)-Appell polynomials and their associated difference equations

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3085-3121
Author(s):  
H.M. Srivastava ◽  
B.Y. Yaşar ◽  
M.A. Özarslan
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Recurrence Relation ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Equivalence Theorem ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Special Case

In the present paper, we introduce and investigate the big (p,q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p,q)- Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p; q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain recurrence relations and difference equations. In the special case when p = 1, we obtain recurrence relations and difference equations which are satisfied by the big q-Bernoulli polynomials and the big q-Euler polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell polynomials reduce to the usual Appell polynomials. Therefore, the recurrence relation and the difference equation obtained for the big (p; q)-Appell polynomials coincide with the recurrence relation and differential equation satisfied by the usual Appell polynomials. In the last section, we have chosen to also point out some obvious connections between the (p; q)-analysis and the classical q-analysis, which would show rather clearly that, in most cases, the transition from a known q-result to the corresponding (p,q)-result is fairly straightforward.

scholarly journals q-Difference equations for the 2-iterated q-Appell and mixed type q-Appell polynomials

2018 ◽  
Vol 8 (1) ◽  
pp. 63-77 ◽  
Author(s):  
H. M. Srivastava ◽  
Subuhi Khan ◽  
Mumtaz Riyasat
Keyword(s):  
Difference Equations ◽  
Mixed Type ◽  
Appell Polynomials

scholarly journals ON A FAMILY OF (p, q)-HYBRID POLYNOMIALS

2021 ◽  
Vol 45 (03) ◽  
pp. 409-426
Author(s):  
GHAZALA YASMIN ◽  
ABDULGHANI MUHYI
Keyword(s):  
Generating Function ◽  
Graphical Representations ◽  
Appell Polynomials ◽  
Function Series ◽  
Definition Of

In this paper, the class of (p,q)-Bessel-Appell polynomials is introduced. The generating function, series definition and determinant definition of this class are established. Certain members of (p,q)-Bessel-Appell polynomials are considered and some properties of these members are also derived. Further, the class of 2D (p,q)-Bessel-Appell polynomials is introduced by means of the generating function and series definition. In addition, the graphical representations of some members of (p,q)-Bessel-Appell polynomials and 2D (p,q)-Bessel-Appell polynomials are plotted with the help of Matlab.

scholarly journals Discrete Hypergeometric Legendre Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2546
Author(s):  
Tom Cuchta ◽  
Rebecca Luketic
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Legendre Polynomials ◽  
Hypergeometric Series ◽  
Recurrence Relations ◽  
Discrete Analog

A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials. We derive their difference equations, recurrence relations, and generating function.

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.

Words

PMLA ◽  
1935 ◽  
Vol 50 (4) ◽  
pp. 1320-1327
Author(s):  
Colbert Searles
Keyword(s):  
Subject Matter ◽  
Assistant Professor ◽  
The Subject

THE germ of that which follows came into being many years ago in the days of my youth as a university instructor and assistant professor. It was generated by the then quite outspoken attitude of colleagues in the “exact sciences”; the sciences of which the subject-matter can be exactly weighed and measured and the force of its movements mathematically demonstrated. They assured us that the study of languages and literature had little or nothing scientific about it because: “It had no domain of concrete fact in which to work.” Ergo, the scientific spirit was theirs by a stroke of “efficacious grace” as it were. Ours was at best only a kind of “sufficient grace,” pleasant and even necessary to have, but which could, by no means ensure a reception among the elected.

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