For questions about the Mittag-Leffler function, a two-parameter function defined by a series that generalizes the exponential one. Particular cases include trigonometric functions, the error function, etc. It is advisable to also use the [special-functions] tag in conjunction with this tag.
The Mittag-Leffler function $E_{\alpha,\beta}(z)$ is an entire function of (a complex variable) $z$, which depends on two parameters $\alpha,\beta\in\mathbb{C}$ with $\Re\alpha>0$, and is defined as $$E_{\alpha,\beta}(z)=\sum_{n=0}^\infty\frac{z^n}{\Gamma(\alpha n+\beta)}$$ where $\Gamma$ is the gamma-function. The case $\beta=1$ is often abbreviated by $E_\alpha(z)=E_{\alpha,1}(z)$.
This series generalizes the exponential one: $e^z=E_1(z)$. More generally, if $\alpha,\beta$ are integers then $E_{\alpha,\beta}(z)$ is a linear combination of (complex) exponentials; say $\cosh z=E_2(z^2)$ and $\cos z=E_2(-z^2)$. Another well-known case $E_{1/2}(z)=e^{z^2}\operatorname{erfc}(-z)$ uses the (complementary) error-function.
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