( s ) = ∑ n = 1 ∞ 1 n s = 11 − 2 1 − s ∑ n = 1 ∞ ( − 1 ) n + 1 n s , {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1-2^{1-s}}}\sum
逻辑斯谛函数是一种常见的S型函数,其公式如下: S ( t ) = 11 + e − t . {\displaystyle S(t)={\frac {1}{1+e^{-t}}}.} 其级数展开为: s := 1 / 2 + 1 4 t − 1 48 t 3 + 1 480 t 5 − 17 80640