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Explicit Expressions for Most Common Entropies [PDF]

Entropy, 2023
Entropies are useful measures of variation. However, explicit expressions for entropies available in the literature are limited. In this paper, we provide a comprehensive collection of explicit expressions for four of the most common entropies for over ...
Saralees Nadarajah, Malick Kebe
doaj   +2 more sources

New series expansions of the Gauss hypergeometric function [PDF]

Advances in Computational Mathematics, 2012
18 pages, 6 figures, 4 tables. In Advances in Computational Mathematics, 2012 Second version with corrected typos in equations (18) and (19)
JOSÉ L Lopez, Nico M Temme
exaly   +4 more sources

On the generalized Gauss hypergeometric function

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2008
In this work the (τ, β)-hypergeometric Gauss function is considered, the basic properties of this function are investigated, some applications are given.
N. A. Virchenko
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On Extensions of Extended Gauss Hypergeometric Function

Communications in Advanced Mathematical Sciences, 2019
The aim of this paper is to introduce a new extensions of extended Gauss hypergeometric function. Certain integral representations, transformation and summation formulas for extended Gauss hypergeometric function are presented and some special cases are ...
Ahmed Ali Atash, Salem Saleh Barahmah, Maisoon Ahmed Kulib   +2 more
doaj   +3 more sources

Numerical methods for the computation of the confluent and Gauss hypergeometric functions [PDF]

Numerical Algorithms, 2016
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric functions in different parameter and variable regimes.
John W Pearson, Sheehan Olver, Mason A Porter   +2 more
exaly   +5 more sources

Exact Expressions for Kullback–Leibler Divergence for Univariate Distributions [PDF]

Entropy
The Kullback–Leibler divergence (KL divergence) is a statistical measure that quantifies the difference between two probability distributions. Specifically, it assesses the amount of information that is lost when one distribution is used to approximate ...
Victor Nawa, Saralees Nadarajah
doaj   +2 more sources

Transformations of some Gauss hypergeometric functions

Journal of Computational and Applied Mathematics, 2005
This paper presents explicit algebraic transformations of some Gauss hypergeometric functions. Specifically, the transformations considered apply to hypergeometric solutions of hypergeometric differential equations with the local exponent differences $1/K,1/L,1/M$ such that $K,L,M$ are positive integers and $1/K+1/L+1/M<1$.
Raimundas Vidunas
exaly   +5 more sources

A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments

Axioms
In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some ...
Yue-Wu Li, Feng Qi
doaj   +3 more sources

Integral Representations of Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers

Mathematics, 2022
Given real parameters a,b,c and integer shifts n1,n2,m, we consider the ratio R(z)=2F1(a+n1,b+n2;c+m;z)/2F1(a,b;c;z) of the Gauss hypergeometric functions.
Alexander Dyachenko, Dmitrii Karp
doaj   +3 more sources

Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

Cumhuriyet Science Journal, 2022
When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright ...
Enes Ata, İ. Onur Kıymaz
doaj   +1 more source