The generalized (two-parameter) Mittag-Leffer function is defined by the power series $$E_{\alpha,\beta} (z) = \sum_{k=0}^\infty z^k / \Gamma(\alpha k + \beta) $$ for complex \(z\) and complex \(\alpha, \beta\) with \(Real(\alpha) > 0\) (only implemented for real valued parameters).
mlf(z, a, b = 1, g = 1)
| z | The argument (real-valued) |
|---|---|
| a, b, g | Parameters of the Mittag-Leffler distribution; see Garrappa |
mlf returns the value of the Mittag-Leffler function.
Garrappa, R. (2015). Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions. SIAM Journal on Numerical Analysis, 53(3), 1350–1369. doi: 10.1137/140971191
The Mittag-Leffler function. MathWorks File Exchange. https://au.mathworks.com/matlabcentral/fileexchange/48154-the-mittag-leffler-function
mlf(2,0.7)#> [1] 20.96643