泰勒展开式又叫幂级数展开法实用幂级数:ex= 1+x+x2/2!+x3/3!+…+xn/n!+…,x∈Rln(1+x)=x-x2/2+x3/3-…+(-1)k-1xk/k, x∈(-1,1)sin x = x-x3/3!+x/5!-…+(-1)k-1x2k-1/(2k-1)!+…, x∈Rcos x = 1-x2/2!+x/4!-…+(-1)kx2k/(2k)!+…, x∈Rarcsin x = x + x3/(2×3) + (1×3)x/(2×4×5) + (1×3×5)x/(2×4×6×7)…+(2k+1)!!×x2k+1/(2k!!×(2k+1))+…, x∈(-1,1)(!!表示双阶乘)arccos x = π/2 -[x + x3/(2×3) + (1×3)x/(2×4×5) + (1×3×5)x/(2×4×6×7)……], x∈(-1,1)arctan x = x - x3/3 + x/5 -…, x∈(-∞,1)sinh x = x+x3/3!+x/5!+…+x2k-1/(2k-1)!+…, x∈Rcosh x = 1+x2/2!+x/4!+…+x2k/(2k)!+…, x∈Rarcsinh x =x - x3/(2×3) + (1×3)x/(2×4×5) -(1×3×5)x/(2×4×6×7)…, x∈(-1,1)arctanh x = x + x3/3 + x/5 + …, x∈(-1,1)