In mathematics, Mittag-Leffler summation is any of several variations of the Borel summation method for summing possibly divergent formal power series, introduced by Gösta Mittag-Leffler (1908) Let be a formal power series in z.
A closely related summation method, also called Mittag-Leffler summation, is given as follows (Sansone & Gerretsen 1960).
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 (as an improper integral).
Then the Mittag-Leffler sum of y is given by When α = 1 this is the same as Borel summation.