scholarly journals ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS

2021 ◽  
Vol 6 (2) ◽  
pp. 852
Author(s):  
UMAR MUHAMMAD ABUBAKAR ◽  
Soraj Patel
Keyword(s):  
Hypergeometric Functions ◽  
Special Functions ◽  
Beta Function ◽  
Integral Representations ◽  
Wright Function ◽  
Confluent Hypergeometric Functions ◽  
Summation Formulas ◽  
Generalized Wright Function ◽  
Beta Error ◽  
Extended Beta Function

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some of its properties such as symmetric properties, summation formulas, integral representations, connection with some other special functions such as classical beta, error, Mittag – Leffler, incomplete gamma, hypergeometric, classical Wright, Fox – Wright, Fox H and Meijer G – functions. Furthermore, the generalized beta function is used to generalize classical and other extended Gauss hypergeometric, confluent hypergeometric, Appell’s and Lauricella’s functions.

scholarly journals A New Extension of Beta and Hypergeometric Functions

2018 ◽  
Author(s):  
Gauhar Rahman ◽  
Gulnaz Kanwal ◽  
Kottakkaran Sooppy Nisar ◽  
Abdul Ghaffar
Keyword(s):  
Beta Distribution ◽  
Hypergeometric Functions ◽  
Mellin Transform ◽  
Beta Function ◽  
Moment Generating Function ◽  
Integral Representations ◽  
Confluent Hypergeometric Functions ◽  
Summation Formulas ◽  
Differentiation Formulas ◽  
Mean Variance

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

scholarly journals Certain investigations in the field of special functions

2020 ◽  
Vol 1 (1) ◽  
pp. 87-98
Author(s):  
Maisoon A. Kulib ◽  
Ahmed A. Al-Gonah ◽  
Salem S. Barahmah
Keyword(s):  
Hypergeometric Function ◽  
Special Functions ◽  
Beta Function ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Confluent Hypergeometric Functions ◽  
Research Fields ◽  
Summation Formulas ◽  
Physical Problems ◽  
Wide Range

Motivated mainly by a variety of applications of Euler's Beta, hypergeometric, and confluent hypergeometric functions together with their extensions in a wide range of research fields such asengineering, chemical, and physical problems. In this paper, we introduce modified forms of some extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function by making use of the idea given in reference \cite{9}. Also, certain investigations including summation formulas, integral representations and Mellin transform of these modified functions are derived. Further, many known results are obtained asspecial cases of our main results.

scholarly journals A new Generalization of Extended Beta and Hypergeometric Functions

2018 ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Gauhar Rahman ◽  
Shahid Mubeen
Keyword(s):  
Hypergeometric Functions ◽  
Beta Function ◽  
Integral Representations ◽  
Summation Formulas ◽  
Extended Beta Function

A new generalization of extended beta function and its various properties,integral representations and distribution are given in this paper. In addition, we establishthe generalization of extended hypergeometric and con uent hypergeometric functionsusing the newly extended beta function. The properties these extended and con uenthypergeometric functions such as integral representations, Mellin transformations, dif-ferentiation formulas, transformation and summation formulas are also investigated.

scholarly journals Further Generalized Beta Function with Three Parameters Mittag- Leffler Function

2018 ◽  
pp. 41-49
Author(s):  
Salem Saleh Barahmah
Keyword(s):  
Mellin Transform ◽  
Beta Function ◽  
Integral Representations ◽  
Summation Formulas ◽  
Extended Beta Function

The purpose of the present paper is to introduce a new extension of extended Beta function by product of two Mittag-Leffler functions. Further, we present certain results including summation formulas, integral representations and Mellin transform.

scholarly journals GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

2011 ◽  
Vol 33 (2) ◽  
pp. 187-206 ◽  
Author(s):  
Dong-Myung Lee ◽  
Arjun K. Rathie ◽  
Rakesh K. Parmar ◽  
Yong-Sup Kim
Keyword(s):  
Hypergeometric Functions ◽  
Beta Function ◽  
Confluent Hypergeometric Functions ◽  
Extended Beta Function

scholarly journals An extension of beta function, its statistical distribution, and associated fractional operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ankita Chandola ◽  
Rupakshi Mishra Pandey ◽  
Ritu Agarwal ◽  
Sunil Dutt Purohit
Keyword(s):  
Beta Function ◽  
Summation Formula ◽  
Moment Generating Function ◽  
Statistical Distribution ◽  
Integral Representations ◽  
Cumulative Distribution ◽  
Fractional Operator ◽  
Confluent Hypergeometric Functions ◽  
Lauricella Function ◽  
Extended Beta Function

AbstractRecently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function.

scholarly journals Extended k-Gamma and k-Beta Functions of Matrix Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1715
Author(s):  
Ghazi S. Khammash ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Gamma Function ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Formula ◽  
Beta Function ◽  
Integral Representations ◽  
Matrix Argument ◽  
Functional Relations

Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

scholarly journals A (p,ν)-extension of Srivastava's triple hypergeometric function H_ B and its properties

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Showkat Ahmad Dar ◽  
R. B. Paris
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Mellin Transform ◽  
Beta Function ◽  
Integral Representations ◽  
Recursion Formulas ◽  
Extended Beta Function ◽  
Extended Function

Abstract In this paper, we obtain a ( p , ν ) {(p,\nu)} -extension of Srivastava’s triple hypergeometric function H B ⁢ ( ⋅ ) {H_{B}(\,\cdot\,)} , by using the extended beta function B p , ν ⁢ ( x , y ) {B_{p,\nu}(x,y)} introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 2017, 2, 91–106]. We give some of the main properties of this extended function, which include several integral representations involving Exton’s hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality.

scholarly journals Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions

2018 ◽  
Author(s):  
Dimiter Prodanov
Keyword(s):  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Operators ◽  
Integral Representations ◽  
Wright Function ◽  
Fractional Differential

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

scholarly journals A Note on the New Extended Beta Function with Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Vandana Palsaniya ◽  
Ekta Mittal ◽  
Sunil Joshi ◽  
D. L. Suthar
Keyword(s):  
Hypergeometric Function ◽  
Beta Function ◽  
Moment Generating Function ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Summation Formulas ◽  
Derivative Formulas ◽  
New Type ◽  
Extended Beta Function ◽  
Transformation Formulas

The purpose of this research is to provide a systematic review of a new type of extended beta function and hypergeometric function using a confluent hypergeometric function, as well as to examine various belongings and formulas of the new type of extended beta function, such as integral representations, derivative formulas, transformation formulas, and summation formulas. In addition, we also investigate extended Riemann–Liouville (R-L) fractional integral operator with associated properties. Furthermore, we develop new beta distribution and present graphically the relation between moment generating function and ℓ .

Sign in / Sign up

Export Citation Format

Share Document