In mathematics, the Mittag-Leffler function E_αβ is special function, a complex function which depends on two complex parameters α and β. It may be defined by the following series when the real part of α is strictly positive:

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( - z²)erfc( - iz) = E_{1 / 2,1}(iz)