June 2025
Intermediate to advanced
515 pages
17h 5m
English
Content preview from Python For Engineering and Scientific Computing
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5.5 Series Expansion
Using the f(x).series(x,x0,n) method, SymPy calculates n members for the series of function f(x) at position x0. Listing 5.14 proves Euler’s formula with the series expansion for the sine and cosine functions:
01 #14_series_expansion.py02 from sympy import *03 x=symbols('x')04 n=1005 a=cos(x).series(x,0,n)06 b=(sin(x)*I).series(x,0,n)07 c=exp(x*I).series(x,0,n)08 d=a+b09 #Output10 print("Series expansion cos\n",a)11 print("\nSeries expansion sin\n",b)12 print("\nSeries expansion cos+sin\n",c)13 print("\nSeries expansion e-function\n",d)
Listing 5.14 Series Expansion
Output
Series expansion cos1 - x**2/2 + x**4/24 ...
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