Work

A Wright-Based Generalization of the Euler Beta Function with Statistical Applications

Year: 2026

Type: article

Abstract: In recent years, special function theory has played an increasingly important role in the development of advanced mathematical models and statistical distributions. In this paper, a new extension of the Euler Beta function is introduced by employing the Wright function as a kernel, leading to the formulation of the Beta–Wright function. Several fundamental properties of the proposed function are systematically investigated, including summation formulas, functional relations, Mellin transforms, integral representations, and derivative formulas. Furthermore, extended forms of Gauss and confluent hypergeometric functions are constructed within this framework. In addition to its theoretical significance, the proposed function is applied to statistical modeling, and the associated distributions are analyzed using graphical and analytical techniques. The obtained results demonstrate that the Beta–Wright function provides a flexible and effective tool for both analytical investigations and statistical applications.

Source: Mathematics

DOI: 10.3390/math14061069

Authors: Layth T. Khudhuir, Hiba F. Al-Janaby, Firas Ghanim, Alina Alb Lupaș

Institutions: University of Baghdad, Northern Technical University, University of Sharjah, University of Oradea

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W7140106736

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