# §7.10 Derivatives

 7.10.1 $\frac{{\mathrm{d}}^{n+1}\operatorname{erf}z}{{\mathrm{d}z}^{n+1}}=(-1)^{n}% \frac{2}{\sqrt{\pi}}H_{n}\left(z\right)e^{-z^{2}},$ $n=0,1,2,\dots$.

For the Hermite polynomial $H_{n}\left(z\right)$ see §18.3.

 7.10.2 $w'\left(z\right)=-2zw\left(z\right)+(2i/\sqrt{\pi}),$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $w\left(\NVar{z}\right)$: Faddeeva (or Faddeyeva) function, $\mathrm{i}$: imaginary unit and $z$: complex variable A&S Ref: 7.1.20 Permalink: http://dlmf.nist.gov/7.10.E2 Encodings: TeX, pMML, png See also: Annotations for §7.10 and Ch.7
 7.10.3 ${{w}^{(n+2)}\left(z\right)+2z{w}^{(n+1)}\left(z\right)+2(n+1){w}^{(n)}\left(z% \right)=0},$ $n=0,1,2,\dots$. ⓘ Symbols: $w\left(\NVar{z}\right)$: Faddeeva (or Faddeyeva) function, $z$: complex variable and $n$: nonnegative integer A&S Ref: 7.1.20 Permalink: http://dlmf.nist.gov/7.10.E3 Encodings: TeX, pMML, png See also: Annotations for §7.10 and Ch.7
 7.10.4 $\displaystyle\frac{\mathrm{d}\mathrm{f}\left(z\right)}{\mathrm{d}z}$ $\displaystyle=-\pi z\mathrm{g}\left(z\right),$ $\displaystyle\frac{\mathrm{d}\mathrm{g}\left(z\right)}{\mathrm{d}z}$ $\displaystyle=\pi z\mathrm{f}\left(z\right)-1.$