泰勒公式
三角函数
[sin x = x - frac{x^2}{3!} + frac{x^5}{5!} + (-1)^{2n-1}frac{x^{2n-1}}{(2n-1)!} + O(x^{2n-1})
]
[cos x = 1 - frac{x^2}{2!} + frac{x^4}{4!} + (-1)^{2n-1}frac{x^{2n}}{(2n)!} + O(x^{2n})
]
[ an x = x + frac{x^3}{3} + frac{2x^5}{15} + O(x^5)
]
[arctan x = x - frac{x^3}{3} + frac{x^5}{5} + O(x^5)
]
[arcsin x = x + frac{x^3}{3!} + O(x^3)
]
[arccos x = frac{pi}{2} - x - frac{x^3}{3} + O(x^3)
]
常用函数
[e^x = 1 + x + frac{x^2}{2} + ...+frac{x^n}{n!} +O(x^n)
]
[ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} +O(x^3)
]
[(1+x)^alpha = 1 + alpha x + frac{alpha(alpha - 1)x^2}{2!}+...+frac{alpha...(alpha-n+1)x^n}{n!}+O(x^n)
]