Formula:10114

Digital Library of Mathematical Functions ID 32.10.E22

${\displaystyle{\displaystyle w(z)=\begin{cases}\dfrac{2\exp\left(z^{2}\right)}{\sqrt{\pi}\left(C-i\operatorname{erfc}\left(iz\right)\right)},&\varepsilon=1,\\ \dfrac{2\exp\left(-z^{2}\right)}{\sqrt{\pi}\left(C-\operatorname{erfc}\left(z\right)\right)},&\varepsilon=-1,\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: real
• ${\displaystyle{\displaystyle\varepsilon=\pm 1}}$: = ε ± 1
• ${\displaystyle{\displaystyle C}}$: constant
 

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