Some New Lower Bounds of the Gamma Function Based on Jensen’s Inequality

The gamma function is a fundamental mathematical function at the heart of centralresults in analysis, algebra, probability and physics. It is therefore important to understand all itsfacets, including its possible bounds of various kinds. In this article, we show how the (probabilityor integral) Jensen inequality can be used to derive lower bounds for this central function.Specifically, we propose alternative proofs for two existing results and establish new lower bounds.In particular, they have the properties of being applicable to all positive real numbers and of beingmore precise than some bounds established in the literature. Where appropriate, the theory isexplained by means of graphical illustrations.