Beta
111109

Generalization of Beta functions in terms of Mittag-Leffler function

Article

Last updated: 24 Dec 2024

Subjects

-

Tags

Mathematics

Abstract

In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated. In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated. In this paper, we give a new generalization of extended beta functions by using generalized Mittag Leffler functions. We investigate its properties and its integral representations. In addition, we establish the generalization of extended hypergeometric and Confluent hypergeometric functions by using the newly extended beta function. Some properties of these extended and Confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are also investigated.

DOI

10.21608/fsrt.2020.39397.1023

Keywords

Beta function, hypergeometric functions, Confluent hypergeometric functions

Authors

First Name

Karima

Last Name

Oraby

MiddleName

M.

Affiliation

El-Salam

Email

koraby83@yahoo.com

City

Suez

Orcid

-

First Name

Ahmed

Last Name

Rizq

MiddleName

-

Affiliation

Mathematics and Computer Science Department, Faculty of Science, Suez University

Email

ahmedrizq00@yahoo.com

City

Suez

Orcid

-

First Name

Ehab

Last Name

Abdelhak

MiddleName

-

Affiliation

Mathematics and Computer Science Department, Faculty of Science, Suez University

Email

ehababdelhak987@gmail.com

City

-

Orcid

-

First Name

Mostafa

Last Name

Taema

MiddleName

-

Affiliation

Mathematics and Computer science Department , Faculty of Science, Suez University

Email

mostafataema3@gmail.com

City

-

Orcid

-

First Name

Moamen

Last Name

Magdy

MiddleName

-

Affiliation

Mathematics and Computer Science Department, Faculty of Science, Suez University

Email

magdymoamen344@gmail.com

City

-

Orcid

-

First Name

Mohamed

Last Name

Khaled

MiddleName

-

Affiliation

Mathematics and Computer Science Department, Faculty of Science, Suez University

Email

arfmhmd718@gmail.com

City

-

Orcid

-

Volume

1

Article Issue

1

Related Issue

16982

Issue Date

2020-09-01

Receive Date

2020-08-20

Publish Date

2020-09-01

Page Start

81

Page End

88

Print ISSN

2682-2962

Online ISSN

2682-2970

Link

https://fsrt.journals.ekb.eg/article_111109.html

Detail API

https://fsrt.journals.ekb.eg/service?article_code=111109

Order

10

Type

Original Article

Type Code

1,029

Publication Type

Journal

Publication Title

Frontiers in Scientific Research and Technology

Publication Link

https://fsrt.journals.ekb.eg/

MainTitle

Generalization of Beta functions in terms of Mittag-Leffler function

Details

Type

Article

Created At

22 Jan 2023