Extension of Beta Function and its Agricultural Applications

Abstract

The first kind of Euler integral, known as the β-function, holds significant importance in various fields such as mathematics, engineering, statistics, and the chemical and physical sciences. Numerous extensions of the classical β-function can be found in the literature. In the realm of mathematics, the β-function plays a crucial role in addressing problems related to probability distribution, quantum mechanics, and fluid mechanics. This study aims to introduce new extensions of the β-function with a specific focus on their applications in agriculture. Additionally, the research delves into the applications of the β-function and explores various types of β-functions in conjunction with other special functions. The study further investigates additional extensions, properties, and mutual relationships, shedding light on recurrence relations and generating functions associated with the extended β-function.