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 $x\ge 0$ and suitably adjusted parameters $\alpha$, $\beta$ and $\gamma$