N维函数的泰勒展开公式一元函数的Taylor级数展开公式i2233,,,,1dxdf(x)(x)df(x)(x)df(x),,。f(x,,x),,,,,?,,xf(x)f(x),,,23i!dx1!dx2!3!dxdx,,i0,二元函数的Taylor级数展开公式i,,,,,1,,f(x,,x,y,,y),,,,xyf(x,y),,,,,i!xyi0,,,2,,,,1,,1,,,,,,,,x,,yf(x,y),f(x,y),,x,,yf(x,y),,,,2!,x,y1!,x,y,,,,3,,1,,,,,?,,x,,yf(x,y),,3!,x,y,,,f(x,y),f(x,y),f(x,y),,x,,y,x,y222,,,,,1f(x,y)f(x,y)f(x,y)22,,,,,,,(x)2xy(y),,22,,,,2!xyxy,,3333,,,,,,1f(x,y)f(x,y)f(x,y)f(x,y)3223,?,,,,,,,,,,(x)3(x)y3x(y)(y),,3223,,,,,,3!xxyxyy,,三元函数的Taylor级数展开公式i,,,,,,1,,f(x,,x,y,,y,z,,z),,,,,,xyzf(x,y,z),,,,,,i!xyzi0,,,,,1,,,,,,f(x,y,z),,x,,y,,zf(x,y,z),,1!,x,y,z,,23,,,,1,,,1,,,,,,,,?,,x,,y,,zf(x,y,z),,x,,y,,zf(x,y,z),,,,2!,x,y,z3!,x,y,z,,,,,f,f,f,f(x,y,z),,x,,y,,z,x,y,z222222,,,,,,,,1ffffff222,?,,,,,,,,,,,,,,,(x)2xy2xz(y)2yz(z),,222,,,,,,2!xyxzyz,,,xyz,,1n元函数的Taylor级数展开公式i,,,,,,1,,。f(x,,x,x,,x,?,x,,x),,,,,,,xx?xf(x,x,?,x),1122nn12n12n,,,,,i!xxxi0,12n,,2