MittagLefflerFunction 2004-12-24 23:22:26 2004-12-24 23:59:12 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The Mittag-Leffler function $E_{\alpha \beta}$ is a complex function which depends on two complex parameters $\alpha$ and $\beta$. It may be defined by the following series when the real part of $\alpha$ is strictly positive: $$E_{\alpha \beta} (z) = \sum_{k=0}^\infty {z^k \over \Gamma (\alpha k + \beta)}$$ In this case, the series converges for all values of the argument $z$, so the Mittag-Leffler function is an entire function.