A HARMONIC MEAN INEQUALITY CONCERNING THE GENERALIZED EXPONENTIAL INTEGRAL FUNCTION
- 21 September 2021
- journal article
- Published by Union of Researchers of Macedonia in Advances in Mathematics: Scientific Journal
- Vol. 10 (9), 3227-3231
- https://doi.org/10.37418/amsj.10.9.11
Abstract
In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where $E_k(s)$ is the generalized exponential integral function, $\Gamma(u,s)$ is the upper incomplete gamma function and $k\in \mathbb{N}$.