An Exploration of Some Special Functions and their Applications
Mfonobong Ukweso Peter

Mfonobong Ukweso Peter, Research Assistant Scholar, Applied Mathematics Research Group, Baum Tenpers Institute, Lagos Nigeria.

Manuscript received on 06 November 2024 | Revised Manuscript received on 10 April 2024 | Manuscript Accepted on 15 May 2024 | Manuscript published on 30 May 2024 | PP: 1-11 | Volume-11 Issue-5, May 2024 | Retrieval Number: 100.1/ijaent.B43291213223 | DOI: 10.35940/ijaent.B4329.11050524

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Abstract: Special functions are a class of mathematical functions that fall outside of ele-mentary functions. They have distinct properties and wide-ranging applications in areas such as engineering, applied mathematics, physics, statistics, economics, and finance. In this research paper, I study two popular special functions: the Gamma function Γ(m) and the Beta function β(m, n). I develop some of their important properties and results, prove these properties, and demonstrate some of their practical applications. Understanding the properties and applications of these functions is vital for solving mathematical problems that arise in practical modeling. This study sheds new light on the significance and versatility of Γ(m) and β(m, n), their applications, and mathematical properties.

Keywords: Special, Functions, Wide-Ranging Applications.
Scope of the Article: Applied Mathematics and Mechanics