PlasmaDispersionFunctions.jl

Julia implementation of the plasma dispersion function

$\it{Z}_n(z)=\frac{1}{\sqrt{\pi}}\int_{\infty}^{\infty}\frac{x^n e^{-x^2}}{x-z}dx$ ,

with a recurrence relation

${\it Z}_n(z) = z {\it Z}_{n-1}(z) + \delta_{0, n \mathrm{mod} 2} 2^{\frac{1-n}{2}} \Pi_{i=1}^{\frac{n-3}{2}} \left( 2i + 1 \right)$ .

and

${\it Z}_0(z) = i \sqrt{\pi} \mathrm{erfcx} \left(-i z \right)$