We consider the asymptotic expansion of the one-parameter Mittag-Leffler functionEa(−x) for x → +∞ as the parameter a → 1. The dominant expansion when0 < a < 1 consists of an algebraic expansion of O(x−1) (which vanishes whena = 1), together with an exponentially small contribution that approaches e−x as a → 1. Here we concentrate on the form of this exponentially small expansion whena approaches the value 1. Numerical examples are presented to illustrate the accuracyof the expansion so obtained.
- Mittag-Leffler function
- Asymptotic expansion
- Exponentially small expansion
- Stokes lines