${\displaystyle \sigma >0}$

${\displaystyle x\in [0;\infty )}$

${\displaystyle {\frac {x\exp \left({\frac {-x^{2}}{2\sigma ^{2}}}\right)}{\sigma ^{2}}}}$

${\displaystyle 1-\exp \left({\frac {-x^{2}}{2\sigma ^{2}}}\right)}$

${\displaystyle \sigma {\sqrt {\frac {\pi }{2}}}}$

${\displaystyle \sigma {\sqrt {\ln(4)}}}$

${\displaystyle \sigma }$

${\displaystyle {\frac {4-\pi }{2}}\sigma ^{2}}$

${\displaystyle {\frac {2{\sqrt {\pi }}(\pi -3)}{(4-\pi )^{3/2}}}}$

${\displaystyle -{\frac {6\pi ^{2}-24\pi +16}{(4-\pi )^{2}}}}$

${\displaystyle 1+\ln \left({\frac {\sigma }{\sqrt {2}}}\right)+{\frac {\gamma }{2}}}$

${\displaystyle 1+\sigma t\,e^{\sigma ^{2}t^{2}/2}{\sqrt {\frac {\pi }{2}}}\left({\textrm {erf}}\left({\frac {\sigma t}{\sqrt {2}}}\right)\!+\!1\right)}$

${\displaystyle 1\!-\!\sigma te^{-\sigma ^{2}t^{2}/2}{\sqrt {\frac {\pi }{2}}}\!\left({\textrm {erfi}}\!\left({\frac {\sigma t}{\sqrt {2}}}\right)\!-\!i\right)}$