## You are here

HomeMittag-Leffler function

## Primary tabs

# 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.

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

33E12*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

Sep 17

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

Sep 17

new question: Harshad Number by pspss

Sep 14

new problem: Geometry by parag