テイラー展開
4 n ( n ! ) 2 ( 2 n + 1 ) x 2 n + 1 for | x | < 1 {\displaystyle \sin ^{-1}x=\sum _{n=0}^{\infty }{\frac {(2n)!}{4^{n}(n!)^{2}(2n+1)}}x^{2n+1}\quad {\mbox{ for }}|x|<1}
cos − 1  x = π 2 − ∑ n = 0 ∞ ( 2 n ) ! 4 n ( n ! ) 2 ( 2 n + 1 ) x 2 n + 1 for | x | < 1 {\displaystyle \cos ^{-1}x={\pi \over 2}-\sum _{n=0}^{\infty }{\frac {(2n)!}{4^{n}(n!)^{2}(2n+1)}}x^{2n+1}\quad {\mbox{ for }}|x|<1}
tan − 1  x = ∑ n = 0 ∞ ( − 1 ) n 2 n + 1 x 2 n + 1 for | x | < 1 {\displaystyle \tan ^{-1}x=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}x^{2n+1}\quad {\mbox{ for }}|x|<1}
W 0 ( x ) = ∑ n = 1 ∞ ( − n ) n − 1 n ! x n for | x | < 1 e {\displaystyle W_{0}(x)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}x^{n}\quad {\mbox{ for }}|x|<{\frac {1}{e}}}