Some new inequalities for the beta function and certain ratios of beta functions

Abstract

In this paper, we present various new inequalities and bounds for the beta function and some other related special functions. A variety of different approaches are used to derive these results, including various results from probability theory, in particular. The new upper and lower bounds for the beta function compare favorably to bounds discussed in various other works. Moreover, the methods of this paper can be used to obtain inequalities for other special functions not discussed in this work.

Keywords

• Beta functions
• Gamma functions
• Chebyshev’s inequality
• Inequalities