f(x) = f(x0) + (x-x0)*f(x).diff(x)|x=x0 + ....
Is there any reason not to allow that rhs as the return for
>>> f(x).series(x)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\core\expr.py", line 2341, in series
s = self.subs(x, rep).series(x, x0=0, n=n, dir='+')
File "sympy\core\expr.py", line 2354, in series
s1 = self._eval_nseries(x, n=n, logx=None)
File "sympy\core\function.py", line 447, in _eval_nseries
supported.'''))
NotImplementedError:
series for user-defined functions are not supported.
Maybe it could return something like this:
>>> def fseries(eq, x0, n):
... return Add(*[(x - x0)**i*Subs(eq.diff(x, i), x, x0) for i in range(n
+ 1)])
>>> pprint(fseries(f(x), 1, 2).doit())
/ 2 \|
2 | d || /d \|
(x - 1) *|---(f(x))|| + (x - 1)*|--(f(x))|| + f(1)
| 2 || \dx /|x=1
\dx /|x=1
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