Rozkład chi

A, B, ν

${\displaystyle f(x)={\frac {\left({\frac {x-A}{B}}\right)^{\nu -1}e^{-{\frac {1}{2}}\left({\frac {x-A}{B}}\right)^{2}}}{2^{{\frac {\nu }{2}}-1}B\Gamma \left({\frac {\nu }{2}}\right)}}}$

${\displaystyle F(x)=\Gamma \left({\frac {\nu }{2}},{\frac {1}{2}}\left({\frac {x-A}{B}}\right)^{2}\right)}$

${\displaystyle A+{\frac {{\sqrt {2}}B\Gamma \left({\frac {\nu +1}{2}}\right)}{\Gamma \left({\frac {\nu }{2}}\right)}}}$

nie może być wyrażona za pomocą funkcji elementarnych

${\displaystyle A+B{\sqrt {\nu -1}}}$

${\displaystyle B^{2}\left[\nu -{\frac {2\Gamma ^{2}\left({\frac {\nu +1}{2}}\right)}{\Gamma ^{2}\left({\frac {\nu }{2}}\right)}}\right]}$

${\displaystyle {\frac {{\sqrt {2}}\left[4\Gamma ^{3}\left({\frac {\nu +1}{2}}\right)+\Gamma ^{2}\left({\frac {\nu }{2}}\right)\left(2\Gamma \left({\frac {\nu +3}{2}}\right)-3\nu \Gamma \left({\frac {\nu +1}{2}}\right)\right)\right]}{\Gamma ^{3}\left({\frac {\nu }{2}}\right)\left[\nu -{\frac {2\Gamma ^{2}\left({\frac {\nu +1}{2}}\right)}{\Gamma ^{2}\left({\frac {\nu }{2}}\right)}}\right]^{\frac {3}{2}}}}}$

${\displaystyle {\frac {2\nu (1-\nu )\Gamma ^{4}\left({\frac {\nu }{2}}\right)-24\Gamma ^{4}\left({\frac {\nu +1}{2}}\right)}{\left[\nu \Gamma ^{2}\left({\frac {\nu }{2}}\right)-2\Gamma ^{2}\left({\frac {\nu +1}{2}}\right)\right]^{2}}}+}$
${\displaystyle +{\frac {8(2\nu -1)\Gamma ^{2}\left({\frac {\nu }{2}}\right)\Gamma ^{2}\left({\frac {\nu +1}{2}}\right)}{\left[\nu \Gamma ^{2}\left({\frac {\nu }{2}}\right)-2\Gamma ^{2}\left({\frac {\nu +1}{2}}\right)\right]^{2}}}}$