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

The gamma function is a fundamental mathematical function at the heart of central results in analysis, algebra, probability and physics. It is therefore important to understand all its facets, including its possible bounds of various kinds. In this article, we show how the (probability or 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 being more precise than some bounds established in the literature. Where appropriate, the theory is explained by means of graphical illustrations.