scholarly journals Construction of a new family of Fubini-type polynomials and its applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
H. M. Srivastava ◽  
Rekha Srivastava ◽  
Abdulghani Muhyi ◽  
Ghazala Yasmin ◽  
Hibah Islahi ◽  
...  
Keyword(s):  
Generating Functions ◽  
Graphical Representation ◽  
Special Functions ◽  
Approximate Solutions ◽  
View Point ◽  
New Class ◽  
New Family ◽  
General Class Of Polynomials ◽  
Operational Technique ◽  
Derivative Formulas

AbstractThis paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown.

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 New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials

2021 ◽  
pp. 15-15
Author(s):  
Yilmaz Simsek
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Umbral Calculus ◽  
Discrete Mathematics ◽  
New Class ◽  
Integral Formulas ◽  
Euler Numbers And Polynomials ◽  
Derivative Formulas ◽  
Special Numbers And Polynomials

By using the calculus of finite differences methods and the umbral calculus, we construct recurrence relations for a new class of special numbers. Using this recurrence relation, we define generating functions for this class of special numbers and also new classes of special polynomials. We investigate some properties of these generating functions. By using these generating functions with their functional equations, we obtain many new and interesting identities and relations related to these classes of special numbers and polynomials, the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers. Finally, some derivative formulas and integral formulas for these classes of special numbers and polynomials are given. In general, this article includes results that have the potential to be used in areas such as discrete mathematics, combinatorics analysis and their applications.

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 A New Generalized Family of Distributions for Lifetime Data

2021 ◽  
Vol 19 (1) ◽  
pp. 2-23
Author(s):  
Maha A. D. Aldahlan ◽  
Mohamed G. Khalil ◽  
Ahmed Z. Afify
Keyword(s):  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Generated Family ◽  
Family Of Distributions

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

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 On generalized Lagrange–Hermite–Bernoulli and related polynomials

2020 ◽  
Vol 23 (2) ◽  
pp. 211-224
Author(s):  
Waseem A. Khan ◽  
M. A. Pathan
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Point Of View ◽  
Generalized Polynomials ◽  
New Class ◽  
The Past ◽  
The Family ◽  
Generating Relations ◽  
High Degree

We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials.

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 Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals Existence and algorithm of solutions for generalized nonlinear variational-like inequalities

2005 ◽  
Vol 2005 (12) ◽  
pp. 1843-1851 ◽  
Author(s):  
Zeqing Liu ◽  
Juhe Sun ◽  
Soo Hak Shim ◽  
Shin Min Kang
Keyword(s):  
Iterative Algorithm ◽  
Recent Literature ◽  
Existence Of Solutions ◽  
Approximate Solutions ◽  
New Class

We introduce and study a new class of generalized nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of generalized nonlinear variational-like inequalities. A new iterative algorithm for finding the approximate solutions of the generalized nonlinear variational-like inequality is given and the convergence of the algorithm is also proved. The results presented in this paper improve and generalize some results in recent literature.

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