scholarly journals Finding Determinant Forms of Certain Hybrid Sheffer Sequences

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1105
Author(s):  
Alansari ◽  
Riyasat ◽  
Khan ◽  
Kazmi
Keyword(s):  
Generating Functions ◽  
Integral Transform ◽  
Matrix Approach ◽  
New Family ◽  
Appell Sequences ◽  
Sheffer Sequences

In this article, the integral transform is used to introduce a new family of extended hybrid Sheffer sequences via generating functions and operational rules. The determinant forms and other properties of these sequences are established using a matrix approach. The correspondingresults for the extended hybrid Appell sequences are also obtained. Certain examples in terms of the members of the extended hybrid Sheffer and Appell sequences are framed. By employing operational rules, the identities involving the Lah, Stirling and Pascal matrices are derived for the aforementioned sequences.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

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 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.

scholarly journals Identities and derivative formulas for the combinatorial and Apostol-Euler type numbers by their generating functions

Filomat ◽  
2018 ◽  
Vol 32 (20) ◽  
pp. 6879-6891
Author(s):  
Irem Kucukoglu ◽  
Yilmaz Simsek
Keyword(s):  
Recurrence Relation ◽  
Generating Functions ◽  
Stirling Numbers ◽  
Bell Numbers ◽  
New Family ◽  
Derivative Formulas ◽  
Combinatorial Sums ◽  
Computation Algorithm ◽  
Fractional Derivative Operators ◽  
And Inversion

The first aim of this paper is to give identities and relations for a new family of the combinatorial numbers and the Apostol-Euler type numbers of the second kind, the Stirling numbers, the Apostol-Bernoulli type numbers, the Bell numbers and the numbers of the Lyndon words by using some techniques including generating functions, functional equations and inversion formulas. The second aim is to derive some derivative formulas and combinatorial sums by applying derivative operators including the Caputo fractional derivative operators. Moreover, we give a recurrence relation for the Apostol-Euler type numbers of the second kind. By using this recurrence relation, we construct a computation algorithm for these numbers. In addition, we derive some novel formulas including the Stirling numbers and other special numbers. Finally, we also some remarks, comments and observations related to our results.

scholarly journals A new family of analytic functions defined by means of Rodrigues type formula

2018 ◽  
Vol 68 (3) ◽  
pp. 607-616
Author(s):  
Rabia Aktaş ◽  
Abdullah Altin ◽  
Fatma Taşdelen
Keyword(s):  
Differential Equations ◽  
Generating Functions ◽  
Analytic Functions ◽  
Recurrence Relations ◽  
Type Formula ◽  
New Family ◽  
Bilateral Generating Functions

Abstract In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also derived. Examples of some members belonging to this family of analytic functions are given and differential equations satisfied by these functions are also obtained.

scholarly journals A TRANSFER MATRIX APPROACH TO THE ENUMERATION OF COLORED LINKS

2001 ◽  
Vol 10 (08) ◽  
pp. 1233-1267 ◽  
Author(s):  
J. L. JACOBSEN ◽  
P. ZINN-JUSTIN
Keyword(s):  
Transfer Matrix ◽  
Generating Functions ◽  
Renormalization Scheme ◽  
Matrix Approach ◽  
Connected Component ◽  
Link Diagrams ◽  
Transfer Matrix Approach ◽  
Associated Matrix ◽  
Alternating Link ◽  
Good Agreement

We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight n to each connected component. Considering more general tetravalent diagrams with self-intersections and tangencies allows us to treat topological (flype) equivalences. This is done by means of a finite renormalization scheme for an associated matrix model. We give results, expressed as polynomials in n, for the various generating functions up to order 19 (2-legged link diagrams), 15 (tangles) and 11 (6-legged links) crossings. The limit n→∞ is solved explicitly. We then analyze the large-order asymptotics of the generating functions. For 0≤n≤2 good agreement is found with a conjecture for the critical exponent, based on the KPZ relation.

scholarly journals Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 173 ◽  
pp. 03024
Author(s):  
Tugal Zhanlav ◽  
Ochbadrakh Chuluunbaatar ◽  
Vandandoo Ulziibayar
Keyword(s):  
Iterative Methods ◽  
Generating Function ◽  
Generating Functions ◽  
Order Of Convergence ◽  
Sufficient Conditions ◽  
Optimal Order ◽  
Eighth Order ◽  
New Family ◽  
Special Cases ◽  
Necessary And Sufficient

In this paper we propose a generating function method for constructing new two and three-point iterations withp(p= 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficient conditions forp-th (p= 4, 8) order convergence of the proposed iterations are given in terms of parameters τnand αn. We also propose some generating functions for τnand αn. We develop a unified representation of all optimal eighth-order methods. The order of convergence of the proposed methods is confirmed by numerical experiments.

scholarly journals The Exponentiated Generalized-G Poisson Family of Distributions

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gokarna R. Aryal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Real World ◽  
Generating Functions ◽  
Real World Data ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

AbstractIn this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

scholarly journals The Weibull-G Poisson Family for Analyzing Lifetime Data

2020 ◽  
pp. 131-148 ◽  
Author(s):  
Haitham Yousof ◽  
Muhammad Mansoor ◽  
Morad Alizadeh ◽  
Ahmed Afify ◽  
Indranil Ghosh
Keyword(s):  
Generating Functions ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Family ◽  
Mathematical Properties ◽  
Independent Identically Distributed ◽  
Family Of Distributions

We study a new family of distributions defined by the minimum of the Poissonrandom number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of theproposed family.

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