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sympy.seriesとsympy.taylorの級数展開の結果の比較¶

Note that to evaluate the Taylor polynomial as an approximation of f, e.g. with polyval(), the coefficients must be reversed, and the point of the Taylor expansion must be subtracted from the argument ( http://docs.sympy.org/dev/modules/mpmath/calculus/approximation.html#taylor-series-taylor )

In [3]:

from sympy import Symbol, exp, series
from sympy.mpmath import polyval,taylor,mp
mp.dps = 15; mp.pretty = True

def getpolyval(f,p,n=6,center=0):
    return polyval(taylor(f,center,n)[::-1],p)

x = Symbol('x')

def f(x):
    return 1/(exp(x)+1)

In [4]:

print series(f(x),x,)
print getpolyval(f,x,n=6).expand()

1/2 - x/4 + x**3/48 - x**5/480 + O(x**6)
-0.00208333333333333*x**5 + 0.0208333333333333*x**3 - 0.25*x + 0.5

In [2]:

print 1./48,-1./480

0.0208333333333 -0.00208333333333

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