MittagLeffler

differint.MittagLeffler(a, b, x, num_terms=50, *, ignore_special_cases=False)

Calculate the 2-parameter Mittag-Leffler function by checking for special cases. If a special case can't be used, then calculate the result using the series definition. It is defined as $E_{\alpha,\beta}(z)=\sum^\inf_{k=0} \frac{z^k}{\Gamma(\alpha k+\beta)}$, but for certain $\alpha$ and $\beta$ this can be reduced to simpler forms.

a : float or complex
The first parameter. Can be any complex or real number.


b : float
The second parameter. Can be any real or complex number.


x : float, list, or 1D-array
The values at which to evaluate Mittag-Leffler function. These can be any real or complex numbers.


num_terms : integer
If the series definition is used, then the number of terms in the series to calculate. Default is 50, much higher than that can cause an overflow in the gamma calculation.


ignore_special_cases : bool
If this is true, the series definition will always be used to calculate the results. The special case calculations are much faster, so this should probably only be used for testing purposes.