Mittag-Leffler summation


In mathematics, Mittag-Leffler summation is any of several variations of the Borel summation method for summing possibly divergent formal power series, introduced by

Definition

Let
be a formal power series in z.
Define the transform of by
Then the Mittag-Leffler sum of y is given by
if each sum converges and the limit exists.
A closely related summation method, also called Mittag-Leffler summation, is given as follows.
Suppose that the Borel transform converges to an analytic function near 0 that can be analytically continued along the positive real axis to a function growing sufficiently slowly that the following integral is well defined. Then the Mittag-Leffler sum of y is given by
When α = 1 this is the same as Borel summation.