PlanetMath: Mittag-Leffler function

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Mittag-Leffler function

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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:

$\displaystyle E_{\alpha \beta} (z) = \sum_{k=0}^\infty {z^k \over \Gamma (\alpha k + \beta)}$

In this case, the series converges for all values of the argument

, so the Mittag-Leffler function is an entire function.

"Mittag-Leffler function" is owned by rspuzio.

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Cross-references: entire function, argument, converges, positive, strictly, real part, series, parameters, complex, complex function
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This is version 2 of Mittag-Leffler function, born on 2004-12-24, modified 2004-12-24.
Object id is 6594, canonical name is MittagLefflerFunction.
Accessed 2271 times total.

Classification:

33E12 (Special functions :: Other special functions :: Mittag-Leffler functions and generalizations)

Pending Errata and Addenda

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