Mittag-leffler Function

In mathematics, the Mittag-Leffler function E_{\alpha \beta} is special function, 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.

Relationship to the error function

The error function is a special case of the Mittag-Leffler function:
w(z)=\exp(-z^2)\mbox{erfc}(-iz) = E_{1/2,1}(iz)

 

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