Real Analysis Exchange

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

Kenneth S. Miller

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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

Permanent link to this document
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

Keywords
{Mittag-Leffler function} {complete monotonicity}

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


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