scholarly journals On Type 2 Degenerate Poly-Frobenius-Genocchi Polynomials and Numbers

2020 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz ◽  
Serkan Araci
Keyword(s):  
Generating Function ◽  
Genocchi Polynomials ◽  
Explicit Expressions

In this paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 degenerate poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we investigate diverse explicit expressions and some identities for those polynomials.

scholarly journals A Note on Type 2 Degenerate Poly-Frobenius-Euler Polynomials

2020 ◽  
Author(s):  
Waseem Khan
Keyword(s):  
Euler Polynomials ◽  
Genocchi Polynomials ◽  
Explicit Expressions

In this paper, we construct the degenerate poly-Frobenius-Genocchi polynomials, called the type 2 degenerate poly-Frobenius-Euler polynomials, by means of polyexponential function. We derive explicit expressions and some identities of those polynomials. In the last section, we introduce type 2 degenerate unipoly-Frobenius-Genocchi polynomials by means of unipoly function and derive explicit multifarious properties.

scholarly journals Construction of the Type 2 Poly-Frobenius-Genocchi Polynomials with Their Certain Applications

2020 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz ◽  
Serkan Araci
Keyword(s):  
Linear Combination ◽  
Generating Function ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Genocchi Polynomials ◽  
Definition Of ◽  
Special Case

Motivated by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim, in the present paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Frobenius-Genocchi polynomias equal a linear combination of the classical Frobenius-Genocchi polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Frobenius-Genocchi polynomials and Bernoulli polynomials of order k. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim, we introduce the unipoly-Frobenius-Genocchi polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Frobenius-Genocchi polynomials and the classical Frobenius-Genocchi polynomials.

Extended criterion for comparison of empirical distributions

1970 ◽  
Vol 7 (01) ◽  
pp. 1-20 ◽  
Author(s):  
Ora Engleberg Percus ◽  
Jerome K. Percus
Keyword(s):  
Sample Size ◽  
Generating Function ◽  
Relative Number ◽  
Function Technique ◽  
Large Sample Size ◽  
Large Sample ◽  
Empirical Distributions ◽  
Asymptotic Problem ◽  
Explicit Expressions

A generating function technique is used to determine the probability that the deviation between two empirical distributions drawn from the same population lies within a given band a specified number of times. We also treat the asymptotic problem of very large sample size, and obtain explicit expressions when the relative number of failures is very small or very large.

scholarly journals Some Identities on the Poly-Genocchi Polynomials and Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1007 ◽  
Author(s):  
Dmitry V. Dolgy ◽  
Lee-Chae Jang
Keyword(s):  
Arithmetic Function ◽  
Bernoulli Polynomials ◽  
Genocchi Polynomials

Recently, Kim-Kim (2019) introduced polyexponential and unipoly functions. By using these functions, they defined type 2 poly-Bernoulli and type 2 unipoly-Bernoulli polynomials and obtained some interesting properties of them. Motivated by the latter, in this paper, we construct the poly-Genocchi polynomials and derive various properties of them. Furthermore, we define unipoly Genocchi polynomials attached to an arithmetic function and investigate some identities of them.

scholarly journals Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Series Representation ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Eulerian Polynomials ◽  
New Class ◽  
Genocchi Polynomials

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

scholarly journals A Note on Type 2 Degenerate Poly-Fubini Polynomials and Numbers

2020 ◽  
Author(s):  
Waseem Khan
Keyword(s):  
Arithmetic Function ◽  
Special Numbers And Polynomials ◽  
Explicit Expressions

In this paper, we construct the degenerate poly-Fubini polynomials, called the type 2 degenerate poly-Fubini polynomials, by using the modified degenerate polyexponential function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we introduce type 2 degenerate unipoly- Fubini polynomials attached to an arithmetic function, by using the modified degenerate polyexponential function and investigate some identities for those polynomials. Furthermore, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

Approximations of Genocchi polynomials of complex order

2020 ◽  
pp. 2150083
Author(s):  
Cristina B. Corcino ◽  
Roberto B. Corcino
Keyword(s):  
Generating Function ◽  
Taylor Expansion ◽  
Contour Integration ◽  
Genocchi Polynomials ◽  
Complex Order ◽  
Approximation Formulas ◽  
Branch Cuts

Approximation formulas for the Genocchi polynomials of complex order are obtained using contour integration with the contour avoiding branch cuts. An alternative expansion is also obtained by expanding a function involving the generating function in a two-point Taylor expansion.

scholarly journals A Parameterized Intuitionistic Type-2 Fuzzy Inference System with Particle Swarm Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 562
Author(s):  
Chun-Min Yu ◽  
Kuo-Ping Lin ◽  
Gia-Shie Liu ◽  
Chia-Hao Chang
Keyword(s):  
Particle Swarm Optimization ◽  
Generating Function ◽  
Fuzzy Inference System ◽  
Medical Diagnosis ◽  
Capacity Planning ◽  
Fuzzy Inference ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Inference System

The aim of this study was to develop a novel intuitionistic Type-2 fuzzy inference system (IT-2 FIS) which adopts a parameterized Yager-generating function and particle swarm optimization (PSO). In IT-2 FIS, the intuitionistic Type-2 is set as a fuzzy symmetrical triangular number in which the hesitation degree adopts the Yager-generating function, and the parameters of the proposed IT-2 FIS adopting the PSO are tuned. The intuitionistic and Type-2 fuzzy sets have been proven to be the most effective for handling more uncertainty. Therefore, this study proposes an intuitionistic Type-2 set with a Yager-generating function to enhance the conventional fuzzy inference system. Moreover, PSO can improve the fuzzy inference system by searching for the optimal parameters of IT-2 FIS. In this study, linguistic variables were represented by triangular fuzzy numbers (TFS). Two numerical examples were examined: capacity-planning and medical diagnosis problems. An approaching capacity-loadings example was used to verify that the proposed IT-2 FIS could effectively estimate the results of the capacity loadings. In the medical diagnosis problem, IT-2 FIS could obtain a higher correct rate by revealing experts’ knowledge. In both examples, the proposed IT-2 FIS provided more objective estimated values than traditional fuzzy inference systems (FIS) and Type-2 FIS.

scholarly journals A note on the generalized q-Genocchi measures with weight

2011 ◽  
Vol 31 (1) ◽  
pp. 17 ◽  
Author(s):  
Hassan Jolany ◽  
Serkan Araci ◽  
Mehmet Acikgoz ◽  
Jong-Jin Seo
Keyword(s):  
Integral Representation ◽  
Generating Function ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
Insight Into

In this paper we investigate special generalized q-Genocchi measures. We introduce q-Genocchi measures with weight alpha. The present paper deals with q-extension of Genocchi measure. Some earlier results of T. Kim in terms of q-Genocchi polynomials can be deduced. We apply the method of generating function, which are exploited to derive further classes of q-Genocchi polynomials and develop q-Genocchi measures. To be more precise, we present the integral representation of p-adic q-Genocchi measure with weight alpha which yields a deeper insight into the effectiveness of this type of generalizations. Generalized q-Genocchi numbers with weight alpha possess a number of interesting properties which we state in this paper.

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