#範例10-5：以泰勒多項式逼近指數函數exp(x)
from sympy import *
x = symbols('x')
f = Function('f')(x)
f = exp(x)
#畫圖比較
ty2 = series(f, x, x0=0, n=3).removeO()
ty4 = series(f, x, x0=0, n=5).removeO()
ty8 = series(f, x, x0=0, n=9).removeO()

p1 = plot(f, ty2, ty4, ty8, (x, -4, 4), show=False)
p1[0].line_color = 'red'
p1[1].line_color = 'blue'
p1[2].line_color = 'green'
p1[3].line_color = 'yellow'
p1[0].label = '$e(x)$'
p1[1].label = '$taylor(n=2)$'
p1[2].label = '$taylor(n=4)$'
p1[3].label = '$taylor(n=8)$'
p1.legend = True
p1.show()