用函数幂 F^g 逼近 e 的分析根据

elim

待续.....

elim

例如 F(n) = 1+f(n), f(n) = 1/n,  g(n) = (n(n+1)(n+1/2))^{1/3},

则 f g = ((1+1/n)(1+1/(2n)))^(1/3) = 1+f/2-f^2/12 +f^3/24+O(f)^4

所以 (1+1/n)^(n(n+1)(n+1/2))^{1/3} = e + O(1/n)^4