On the complete monotonicity of the three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$

Abstract

Using the Bernstein theorem we give a simple proof of the complete monotonicity of the three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ and $\gamma$