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 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.

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.

scholarly journals INCOMPLETE BESSEL POLYNOMIALS: A NEW CLASS OF SPECIAL POLYNOMIALS FOR ELECTROMAGNETICS

2015 ◽  
Vol 41 ◽  
pp. 85-93 ◽  
Author(s):  
Diego Caratelli ◽  
Galina Babur ◽  
Alexander A. Shibelgut ◽  
Oleg Stukach
Keyword(s):  
Bessel Polynomials ◽  
New Class ◽  
Special Polynomials

scholarly journals Generating Functions for Orthogonal Polynomials of A2, C2 and G2

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 354 ◽  
Author(s):  
Tomasz Czyżycki ◽  
Jiří Hrivnák ◽  
Jiří Patera
Keyword(s):  
Orthogonal Polynomials ◽  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Bell Polynomials ◽  
The Third ◽  
Weight Lattice ◽  
Hybrid Character ◽  
Polynomial Family

The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical univariate Chebyshev polynomials of the third and fourth kinds. Explicit evaluating formulas for each polynomial family are derived and linked to the incomplete exponential Bell polynomials.

scholarly journals Some properties of generalized hypergeometric Appell polynomials

2020 ◽  
Vol 12 (1) ◽  
pp. 129-137 ◽  
Author(s):  
L. Bedratyuk ◽  
N. Luno
Keyword(s):  
Differential Operator ◽  
Power Series ◽  
Hypergeometric Function ◽  
Explicit Formula ◽  
Series Representation ◽  
Generalized Hypergeometric Function ◽  
Appell Polynomials ◽  
Pochhammer Symbol ◽  
Formal Power ◽  
Polynomial Family

Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$. In this paper, we present a new real-valued Appell-type polynomial family $A_n^{(k)}(m,x)$, $n, m \in {\mathbb{N}}_0$, $k \in {\mathbb{N}},$ every member of which is expressed by mean of the generalized hypergeometric function ${}_{p} F_q \begin{bmatrix} \begin{matrix} a_1, a_2, \ldots, a_p \:\\ b_1, b_2, \ldots, b_q \end{matrix} \: \Bigg| \:z \end{bmatrix}= \sum\limits_{k=0}^{\infty} \frac{a_1^{(k)} a_2^{(k)} \ldots a_p^{(k)}}{b_1^{(k)} b_2^{(k)} \ldots b_q^{(k)}} \frac{z^k}{k!}$ as follows $$ A_n^{(k)}(m,x)= x^n{}_{k+p} F_q \begin{bmatrix} \begin{matrix} {a_1}, {a_2}, {\ldots}, {a_p}, {\displaystyle -\frac{n}{k}}, {\displaystyle -\frac{n-1}{k}}, {\ldots}, {\displaystyle-\frac{n-k+1}{k}}\:\\ {b_1}, {b_2}, {\ldots}, {b_q} \end{matrix} \: \Bigg| \: \displaystyle \frac{m}{x^k} \end{bmatrix} $$ and, at the same time, the polynomials from this family are Appell-type polynomials. The generating exponential function of this type of polynomials is firstly discovered and the proof that they are of Appell-type ones is given. We present the differential operator formal power series representation as well as an explicit formula over the standard basis, and establish a new identity for the generalized hypergeometric function. Besides, we derive the addition, the multiplication and some other formulas for this polynomial family.

A new class of score generating functions for regression models

2002 ◽  
Vol 57 (2) ◽  
pp. 205-214 ◽  
Author(s):  
Young Hun Choi ◽  
Ömer Öztürk
Keyword(s):  
Generating Functions ◽  
Regression Models ◽  
New Class

Biosimilars

2017 ◽  
pp. 171-188
Author(s):  
Anil K. Sharma ◽  
Raj K. Keservani ◽  
Rajesh K. Kesharwani
Keyword(s):  
Renal Failure ◽  
Present Article ◽  
Recombinant Dna ◽  
Recombinant Dna Technology ◽  
New Class ◽  
Patients With Diabetes ◽  
Dna Technology ◽  
Live Organism

Biosimilars are a new class of drugs, which are derived from live organism through the recombinant DNA technology. These are recently introduced in the pharmaceutical field for the preparation of drug to prevent or control the diseases. Patients with diabetes and renal failure may already be receiving biosimilar epoetin and may receive same insulin in coming years. The main aim of present article is to introduce the fundamentals of biologics and to explain how they are different and what these differences mean for pharmacists.

A New Class of Generating Functions for Hypergeometric Polynomials

1970 ◽  
Vol 25 (2) ◽  
pp. 405
Author(s):  
David Zeitlin
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Hypergeometric Polynomials

scholarly journals A new family of combinatorial numbers and polynomials associated with peters numbers and polynomials

2020 ◽  
pp. 42-42
Author(s):  
Yilmaz Simsek
Keyword(s):  
Generating Functions ◽  
Fibonacci Numbers ◽  
Recurrence Formula ◽  
Binomial Coefficients ◽  
Combinatorial Identity ◽  
Lucas Numbers ◽  
Fundamental Properties ◽  
Special Polynomials ◽  
New Family ◽  
Special Numbers And Polynomials

The aim of this paper is to define new families of combinatorial numbers and polynomials associated with Peters polynomials. These families are also a modification of the special numbers and polynomials in [11]. Some fundamental properties of these polynomials and numbers are given. Moreover, a combinatorial identity, which calculates the Fibonacci numbers with the aid of binomial coefficients and which was proved by Lucas in 1876, is proved by different method with the help of these combinatorial numbers. Consequently, by using the same method, we give a new recurrence formula for the Fibonacci numbers and Lucas numbers. Finally, relations between these combinatorial numbers and polynomials with their generating functions and other well-known special polynomials and numbers are given.

Sign in / Sign up

Export Citation Format

Share Document