# 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:

$${E}_{\alpha \beta}(z)=\sum _{k=0}^{\mathrm{\infty}}\frac{{z}^{k}}{\mathrm{\Gamma}(\alpha k+\beta )}$$ |

In this case, the series converges for all values of the argument $z$, so the Mittag-Leffler function is an entire function^{}.

Title | Mittag-Leffler function |
---|---|

Canonical name | MittagLefflerFunction |

Date of creation | 2013-03-22 14:54:34 |

Last modified on | 2013-03-22 14:54:34 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 5 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 33E12 |