# §7.4 Symmetry

 7.4.1 $\displaystyle\mathop{\mathrm{erf}\/}\nolimits\!\left(-z\right)$ $\displaystyle=-\mathop{\mathrm{erf}\/}\nolimits\!\left(z\right),$ Symbols: $\mathop{\mathrm{erf}\/}\nolimits\NVar{z}$: error function and $z$: complex variable A&S Ref: 7.1.9 Permalink: http://dlmf.nist.gov/7.4.E1 Encodings: TeX, pMML, png See also: Annotations for 7.4 7.4.2 $\displaystyle\mathop{\mathrm{erfc}\/}\nolimits\!\left(-z\right)$ $\displaystyle=2-\mathop{\mathrm{erfc}\/}\nolimits\!\left(z\right),$ Symbols: $\mathop{\mathrm{erfc}\/}\nolimits\NVar{z}$: complementary error function and $z$: complex variable Permalink: http://dlmf.nist.gov/7.4.E2 Encodings: TeX, pMML, png See also: Annotations for 7.4 7.4.3 $\displaystyle\mathop{w\/}\nolimits\!\left(-z\right)$ $\displaystyle=2e^{-z^{2}}-\mathop{w\/}\nolimits\!\left(z\right).$ Symbols: $\mathop{w\/}\nolimits\!\left(\NVar{z}\right)$: complementary error function, $\mathrm{e}$: base of exponential function and $z$: complex variable A&S Ref: 7.1.11 Permalink: http://dlmf.nist.gov/7.4.E3 Encodings: TeX, pMML, png See also: Annotations for 7.4 7.4.4 $\displaystyle\mathop{F\/}\nolimits\!\left(-z\right)$ $\displaystyle=-\mathop{F\/}\nolimits\!\left(z\right).$ Symbols: $\mathop{F\/}\nolimits\!\left(\NVar{z}\right)$: Dawson’s integral and $z$: complex variable Permalink: http://dlmf.nist.gov/7.4.E4 Encodings: TeX, pMML, png See also: Annotations for 7.4
 7.4.5 $\displaystyle\mathop{C\/}\nolimits\!\left(-z\right)$ $\displaystyle=-\mathop{C\/}\nolimits\!\left(z\right),$ $\displaystyle\mathop{S\/}\nolimits\!\left(-z\right)$ $\displaystyle=-\mathop{S\/}\nolimits\!\left(z\right),$ Symbols: $\mathop{C\/}\nolimits\!\left(\NVar{z}\right)$: Fresnel integral, $\mathop{S\/}\nolimits\!\left(\NVar{z}\right)$: Fresnel integral and $z$: complex variable A&S Ref: 7.3.17 Permalink: http://dlmf.nist.gov/7.4.E5 Encodings: TeX, TeX, pMML, pMML, png, png See also: Annotations for 7.4
 7.4.6 $\displaystyle\mathop{C\/}\nolimits\!\left(iz\right)$ $\displaystyle=i\mathop{C\/}\nolimits\!\left(z\right),$ $\displaystyle\mathop{S\/}\nolimits\!\left(iz\right)$ $\displaystyle=-i\mathop{S\/}\nolimits\!\left(z\right).$ Symbols: $\mathop{C\/}\nolimits\!\left(\NVar{z}\right)$: Fresnel integral, $\mathop{S\/}\nolimits\!\left(\NVar{z}\right)$: Fresnel integral and $z$: complex variable A&S Ref: 7.3.18 Referenced by: §7.4 Permalink: http://dlmf.nist.gov/7.4.E6 Encodings: TeX, TeX, pMML, pMML, png, png See also: Annotations for 7.4
 7.4.7 $\displaystyle\mathop{\mathrm{f}\/}\nolimits\!\left(iz\right)$ $\displaystyle=(1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\mathop{% \mathrm{f}\/}\nolimits\!\left(z\right),$ $\displaystyle\mathop{\mathrm{g}\/}\nolimits\!\left(iz\right)$ $\displaystyle=(1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\mathop% {\mathrm{g}\/}\nolimits\!\left(z\right).$
 7.4.8 $\displaystyle\mathop{\mathrm{f}\/}\nolimits\!\left(-z\right)$ $\displaystyle=\sqrt{2}\mathop{\cos\/}\nolimits\!\left(\tfrac{1}{4}\pi+\tfrac{1% }{2}\pi z^{2}\right)-\mathop{\mathrm{f}\/}\nolimits\!\left(z\right),$ $\displaystyle\mathop{\mathrm{g}\/}\nolimits\!\left(-z\right)$ $\displaystyle=\sqrt{2}\mathop{\sin\/}\nolimits\!\left(\tfrac{1}{4}\pi+\tfrac{1% }{2}\pi z^{2}\right)-\mathop{\mathrm{g}\/}\nolimits\!\left(z\right).$