The Bigamma function and some of its related inequalities

Year 2025, Volume: 54 Issue: 5, 1774 - 1782, 29.10.2025

Mustapha Raıssoulı , Chergui Mohamed

https://doi.org/10.15672/hujms.1490373

Abstract

In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new function to the standard Beta function have been provided. We have also established inequalities, which allow to approximate this new function.

Keywords

gamma function , bigamma function , special functions

References

• [1] G. E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, 1999.
• [2] R. Beals and R. Wong, Special Functions and Orthogonal Polynomials, Cambridge University Press, 2016.
• [3] M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math. 55, 99-124, 1994.
• [4] S. S. Dragomir, R. P. Agarwal, and N. S. Barnett, Inequalities for beta and gamma functions via some classical and new integral inequalities, J. Inequal. Appl. 5, 103-165, 2000.
• [5] A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics, A Unified Introduction with Applications, Birkhäuser Boston, MA, 1988.
• [6] F. W. J. Olver, Asymptotics and Special Functions, Academic Press Elsevier, 1974
• [7] E. Özergin, M. A. Özarslan, and A. Altin, Extensions of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235 (16), 4601-4610, 2011.
• [8] M. Raïssouli and M. Chergui, Some inequalities for an extended beta function, Int. J. Appl. Math. 34 (4), 721-743, 2021.
• [9] M. Raïssouli and M. Chergui, On some inequalities involving Beta-Logarithmic function, Gulf J. Math. 16 (1), 177-192, 2024.
• [10] C. Viola, An Introduction to Special Functions, Springer Cham, 2016.
• [11] D. G. Zill and M. R. Cullen, Advanced Engineering Mathematics, Jones and Bartlett, Boston 2005.