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# Mittag-Leffler function

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.

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## Mathematics Subject Classification

33E12*no label found*

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