法捷耶娃函数

法捷耶娃函数(Fadeeva function)是一种在等离子物理学中见到的特殊函数，与福格特函数有关，定义如下^[1]

Fadeeva Function

w(z):=e^{-z^{2}}\operatorname {erfc} (-iz)=\operatorname {erfcx} (-iz)=e^{-z^{2}}\left(1+{\frac {2i}{\sqrt {\pi }}}\int _{0}^{z}e^{t^{2}}{\text{d}}t\right).

与福格特函数的关系

w(x+iy)=U(x,y)+iV(x,y)

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^ V. N. Faddeeva and N. N. Terent'ev: Tables of values of the function w(z)=\exp(-z^2)(1+2i/\sqrt{\pi}\int_0^z\exp(t^2)\text{d}t) for complex argument. Gosud. Izdat. Teh.-Teor. Lit., Moscow, 1954; English transl., Pergamon Press, New York, 1961. Unverified citation, copied from Poppe and Wijers (1990)