erfc ( x ) = 2 π ∫ x ∞ e − t 2 d t = e − x 2 x π ∑ n = 0 ∞ ( − 1 ) n ( 2 n ) ! n ! ( 2 x ) 2 n {\displaystyle \operatorname {erfc} (x)={\frac {2}{\sqrt {\pi }}}\int _{x}^{\infty }e^{-t^{2}}\,dt={\frac {e^{-x^{2}}}{x{\sqrt {\pi }}}}\sum _{n=0}^{\infty }(-1)^{n}{\frac {(2n)!}{n!(2x)^{2n}}}}
π = 3 4 3 + 24 ∫ 0 1 / 4 x − x 2 d x {\displaystyle {\pi }={\frac {3}{4}}{\sqrt {3}}+24{\int _{0}^{1/4}}{{\sqrt {x-x^{2}}}dx}}
3 x − 1 + ( 1 + x ) 2 {\displaystyle {\sqrt {3x-1}}+(1+x)^{2}}
