Question Number 91223 by M±th+et+s last updated on 28/Apr/20
$${what}\:{is}\:{complementary}\:{error}\:{function} \\ $$$${erfc}\left({t}\right)? \\ $$
Answered by MJS last updated on 28/Apr/20
$$\mathrm{erf}\:{x}\:=\frac{\mathrm{2}}{\sqrt{\pi}}\underset{\mathrm{0}} {\overset{{x}} {\int}}\mathrm{e}^{−{t}^{\mathrm{2}} } {dt}=\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\pi}}\Gamma\:\left(\frac{\mathrm{1}}{\mathrm{2}}\mid{x}^{\mathrm{2}} \right) \\ $$$$\mathrm{erfc}\:{x}\:=\mathrm{1}−\mathrm{erf}\:{x} \\ $$$$\mathrm{erfi}\:{x}\:=−\mathrm{i}\:\mathrm{erf}\:\left(\mathrm{i}{x}\right) \\ $$
Commented by M±th+et+s last updated on 28/Apr/20
$${thank}\:{you}\:{sir}\: \\ $$