f ( x ) = x 2 {\displaystyle f(x)=x^{2}}
f ( x ) {\displaystyle f(x)\,\!} = ∑ n = 0 ∞ a n x n {\displaystyle =\sum _{n=0}^{\infty }a_{n}x^{n}} = a 0 + a 1 x + a 2 x 2 + ⋯ {\displaystyle =a_{0}+a_{1}x+a_{2}x^{2}+\cdots }
( 1 2 ) n {\displaystyle \left({\frac {1}{2}}\right)^{n}}
∑ m = 1 ∞ ∑ n = 1 ∞ m 2 n 3 m ( m 3 n + n 3 m ) {\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}n}{3^{m}\left(m3^{n}+n3^{m}\right)}}}
| z ¯ | = | z | , | ( z ¯ ) n | = | z | n , arg ( z n ) = n arg ( z ) {\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}
(1)
f ( x ) = { 1 − 1 ≤ x < 0 1 2 x = 0 1 − x 2 otherwise {\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&{\text{otherwise}}\end{cases}}}
