Unit.
series
(x=None, x0=0, n=6, dir='+', logx=None)¶Series expansion of “self” around x = x0
yielding either terms of
the series one by one (the lazy series given when n=None), else
all the terms at once when n != None.
Returns the series expansion of “self” around the point x = x0
with respect to x
up to O((x - x0)**n, x, x0)
(default n is 6).
If x=None
and self
is univariate, the univariate symbol will
be supplied, otherwise an error will be raised.
>>> from sympy import cos, exp
>>> from sympy.abc import x, y
>>> cos(x).series()
1 - x**2/2 + x**4/24 + O(x**6)
>>> cos(x).series(n=4)
1 - x**2/2 + O(x**4)
>>> cos(x).series(x, x0=1, n=2)
cos(1) - (x - 1)*sin(1) + O((x - 1)**2, (x, 1))
>>> e = cos(x + exp(y))
>>> e.series(y, n=2)
cos(x + 1) - y*sin(x + 1) + O(y**2)
>>> e.series(x, n=2)
cos(exp(y)) - x*sin(exp(y)) + O(x**2)
If n=None
then a generator of the series terms will be returned.
>>> term=cos(x).series(n=None)
>>> [next(term) for i in range(2)]
[1, -x**2/2]
For dir=+
(default) the series is calculated from the right and
for dir=-
the series from the left. For smooth functions this
flag will not alter the results.
>>> abs(x).series(dir="+")
x
>>> abs(x).series(dir="-")
-x