## Real Analysis Exchange

### A Note on the Complete Monotonicity of the Generalized Mittag-Leffler Function

Kenneth S. Miller

#### Abstract

If $E_{\alpha,\beta}(x)$ is the generalized Mittag-Leffler function, then the complete monotonicity of $E_{\alpha,\beta}(-x)$ for $0\le\alpha\le1$, $\beta\ge\alpha$ is an immediate corollary of a 1948 result due to Pollard. The proof can be accomplished within the framework of real analysis.

#### Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 753-756.

Dates
First available in Project Euclid: 14 May 2012

https://projecteuclid.org/euclid.rae/1337001380

Mathematical Reviews number (MathSciNet)
MR1639957

Zentralblatt MATH identifier
0964.33011

Subjects
Primary: 33E20: Other functions defined by series and integrals

#### Citation

Miller, Kenneth S. A Note on the Complete Monotonicity of the Generalized Mittag-Leffler Function. Real Anal. Exchange 23 (1999), no. 2, 753--756. https://projecteuclid.org/euclid.rae/1337001380