A Note on the Theory of Gamma and Beta Functions

Year 2022, Issue: 45, 60 - 63, 31.12.2022

Nihal Özdoğan

https://doi.org/10.31590/ejosat.1219501

Abstract

Fizik ve mühendislik problemleri detaylı bir uygulamalı matematik bilgisini ve gamma ve beta fonksiyonları gibi özel fonksiyonların anlaşılmasını gerektirir. Özel fonksiyonlar konusu çok önemlidir ve uygulamalı bilimlerdeki yeni problemlerin varlığı ile sürekli genişlemektedir. Biz bu makalede, gamma ve beta fonksiyonlarının temel teorisini, birbirleriyle olan bağlantılarını ve mühendislik problemlerine uygulanabilirliklerini açıklıyoruz.

Keywords

Beta Function, Gamma Function, Applied Mathematics, Engineering.

A Note on the Theory of Gamma and Beta Functions

Abstract

Physics and engineering problems require a detailed knowledge of applied mathematics and an understanding of special functions such as gamma and beta functions. The topic of special functions is very important and it is constantly expanding with the existence of new problems in the applied sciences. In this article, we describe the basic theory of gamma and beta functions, their connections with each other and their applicability to engineering problems.

Keywords

Beta Function, Gamma Function, Applied Mathematics, Engineering.

References

• Bell, W.W. (1968). Special Functions for Scientists and Engineers. Courier Corporation, D. Van Nostrand Company, London.
• Chaudry, M.A., Qadir A., Rafique, M., & Zubair, S.M. (1997). Extension of Euler’s beta function. Journal of Computational and Applied Mathematics, 78, 19-32.
• Euler, L. (1729). Letter to Goldbach, Oct. 13. Correspondence math. et phys. de quelques celebres geometres du 18e siecle, publiee par Fuss, vol. 1 (St. PMtersburg, 1843).
• Euler. L. (1729). De progressionibus transcendentibus sen quaroum termini generales algebrare dari nequeunt, (1738). Commentarii academiae scientiarum Petropolitanae, 5, 36-57, presented to the St. Petersburg Academy on November 28.
• Euler, L. (1771). Evolutio formulae integralis int xˆ(f-1) dx (lx)ˆ(m/n) integratione a valore x= 0 ad x= 1 extensa. Novi Commentarii Academiae Scientiarum Petropolitanae, 16, 91-139.
• Jaabar, S. M., & Hussain, A. H. (2021). Special Functions and Their Applications. International Journal of Engineering and Information Systems, Volume 5, 18-21.
• Legendre, A.M. (1814). Exercises de calcul integral. 2 vols. Courcier, Paris.
• Luke, Y.L. (1969). Special functions and their approximations. Vol. 1, Academic press.
• Naresh, D., & Umar, M.A. (2021). A further Extension of Gamma and Beta Functions involving Generalized Mittag-Leffler Function and its Applications. Journal of Physical Sciences, Volume 26, 61-71.
• Pochhammer, L. (1870). Ueber Hypergeometrischen Funktionen Hoheren Ordungen. Journal fr die Reine und Angewandte Mathematik, 71(216).
• Rahul, G., Praveen A., Georgia, I.O., & Shilpi, J. (2022). Extended Beta and Gamma Matrix Functions via 2-Parameter Mittag-Leffler Matrix Function. Mathematics, 10, 892.
• Ricardo, Perez-Marco. (2021). On the Definition of Euler Gamma Function. Temme, N. M. (2011). Special functions: An introduction to the classical functions of mathematical physics. John Wiley & Sons.
• Whittaker, E.T. (1902). A Course of Modern Analysis: An Introduction to the General Theory of Infinite Series and of Analytic Functions, with an Account of the Principal Transcendental Functions. University Press.
• Whittaker, E. T., & Watson, G. N. (1927). A course of modern analysis. Cambridge university press; Reprinted by Cambridge university press in 1927.