scholarly journals On Fully Degenerate Daehee Numbers and Polynomials of the Second Kind

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Sang Jo Yun ◽  
Jin-Woo Park
Keyword(s):  
Exponential Function ◽  
Special Functions ◽  
Eulerian Numbers

In a study, Carlitz introduced the degenerate exponential function and applied that function to Bernoulli and Eulerian numbers and degenerate special functions have been studied by many researchers. In this paper, we define the fully degenerate Daehee polynomials of the second kind which are different from other degenerate Daehee polynomials and derive some new and interesting identities and properties of those polynomials.

scholarly journals Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables

2020 ◽  
pp. 75-80
Author(s):  
I. Teteruk
Keyword(s):  
Exponential Function ◽  
Hypergeometric Series ◽  
Special Functions ◽  
Basic Hypergeometric Series ◽  
Padé Approximants ◽  
Two Dimensional ◽  
Rational Approximants ◽  
One Dimensional ◽  
Pade Approximants ◽  
Function Of Two Variables

Generalized instantaneous image were introduced by V.K. Dzyaduk [1] in 1981 and proved to be a convenient tool for constructing and studying the Padé approximants and their generalizations (see [2]). The method of generalized instantaneous images proposed by Dzyadyk made it possible to construct and study rational Padé approximants and their generalizations for many classes of special functions from a single position. As an example, the Padé approximants is constructed for a class of basic hypergeometric series, which includes a q-analogue of the exponential function. In this paper the construction of the Pade approximants for the function of two variables is investigated. A two-dimensional functional sequence is constructed, which has a generalized instantaneous image, and rational approximants are determined, which will be generalizations of one-dimensional Padé approximants. The function of the two variables is entirely related to the basic hypergeometric series.

scholarly journals EXCEL-orientated procedure for calculating the values of special functions with interval argument assigned on the hyperbolic form

2021 ◽  
Vol 5 (4) ◽  
pp. 116-123
Author(s):  
Valeriy Dubnitskiy ◽  
Anatolii Kobylin ◽  
Oleg Kobylin ◽  
Yuriy Kushneruk
Keyword(s):  
Exponential Function ◽  
Gamma Function ◽  
Special Functions ◽  
Beta Function ◽  
Digamma Function ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Hyperbolic Form ◽  
Hyperbolic Trigonometry ◽  
Integral Exponential Function

Aim of the work is to propose the main terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form. The results of the work. The methods of presenting the interval values in the hyperbolic form and the rules of addition, subtraction, multiplication, and division of this values were considered. The procedures of calculating the function values, whose arguments can be degenerate or interval values were described. Namely, the direct and the reverse functions of the linear trigonometry, the direct and the reverse functions of the hyperbolic trigonometry, exponential function, arbitrary exponential function and power function, Gamma-function, incomplete Gamma-function, digamma-function, trigamma-function, tetragamma-function, pentagamma-function, Beta-function and its partial derivatives, integral exponential function, integral logarithm, dilogarithm, Frenel integrals, sine integral, cosine integral, hyperbolic sine integral, hyperbolic cosine integral. The basic terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form were proposed. The numerical examples were provided, that illustrate the application of the proposed methods.

scholarly journals Unified integral associated with the generalized V-function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. Chandak ◽  
S. K. Q. Al-Omari ◽  
D. L. Suthar
Keyword(s):  
Bessel Function ◽  
Hypergeometric Function ◽  
Exponential Function ◽  
Special Functions ◽  
General Nature ◽  
Generalized Hypergeometric Function ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Special Cases ◽  
Lommel Function

Abstract In this paper, we present two new unified integral formulas involving a generalized V-function. Some interesting special cases of the main results are also considered in the form of corollaries. Due to the general nature of the V-function, several results involving different special functions such as the exponential function, the Mittag-Leffler function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function and the generalized hypergeometric function are obtained by specializing the parameters in the presented formulas. More results are also discussed in detail.

scholarly journals The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V -Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
S. Chandak ◽  
Biniyam Shimelis ◽  
Nigussie Abeye ◽  
A. Padma
Keyword(s):  
Fractional Calculus ◽  
Bessel Function ◽  
Hypergeometric Function ◽  
Exponential Function ◽  
Special Functions ◽  
Generalized Hypergeometric Function ◽  
Generalized Bessel Function ◽  
Fractional Calculus Operators

In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with V -function as the kernel. In addition, on account of V -function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.

scholarly journals Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function

2021 ◽  
Vol 26 (3) ◽  
pp. 58
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Exponential Function ◽  
Special Functions ◽  
Rational Functions ◽  
Definite Integral ◽  
Fundamental Constants ◽  
Definite Integrals ◽  
Special Cases ◽  
Quotient Of Functions ◽  
Integral Formulae

This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving fundamental constants. The goal of this paper is to expand upon current tables of definite integrals with the aim of assisting researchers in need of new integral formulae.

Distribution and Correlation of the Coding Sequence Lengths in Bacterial Genomes

2008 ◽  
Vol 59 (11) ◽  
Author(s):  
Vasile V. Morariu
Keyword(s):  
Correlation Analysis ◽  
Exponential Function ◽  
Short Range ◽  
Statistical Physics ◽  
Bacterial Genomes ◽  
Coding Sequence ◽  
Correlation Properties ◽  
Short Range Correlations ◽  
Fluctuating System

The length of coding sequence (CDS) series in bacterial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlation properties of CDS for 47 genomes were investigated. The distribution was found to be approximated by an exponential function while the correlation analysis revealed short range correlations.

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