Euler Integrals and Their Applications
Keywords:
Euler integrals, Gamma function, Beta function, mathematical analysis, special functions, differential equations, probability theory, applied mathematicsAbstract
This study examines the theoretical foundations and practical applications of Euler integrals, focusing on their role in modern mathematical analysis. Special attention is given to the Gamma and Beta functions as fundamental representations of Euler integrals. The research explores their properties, interrelationships, and effectiveness in solving complex integrals and differential equations. Additionally, the study highlights their applications in physics, engineering, and probability theory. The results demonstrate that Euler integrals serve as a crucial link between theoretical concepts and real-world problem-solving, making them indispensable in both scientific research and applied fields.
References
1. Abramowitz, M., & Stegun, I. A. (1965). Handbook of mathematical functions with formulas, graphs, and mathematical tables (pp. 253–307). New York, NY: Dover Publications.
2. Artin, E. (2015). The Gamma function (pp. 1–45). Providence, RI: American Mathematical Society.
3. Davis, H. T. (1933). The theory of the Gamma function (pp. 12–78). Bloomington, IN: Principia Press.
4. Rainville, E. D. (1960). Special functions (pp. 25–89). New York, NY: Macmillan.
5. Spiegel, M. R., Lipschutz, S., & Liu, J. (2013). Mathematical handbook of formulas and tables (4th ed., pp. 101–156). New York, NY: McGraw-Hill.
