Comment #6 on issue 905 by pr...@goodok.ru: series error: maximum recursion
depth exceeded
http://code.google.com/p/sympy/issues/detail?id=905
I have carried out more tests and detected.
Master branch:
>>> acos(1-x).series(x)
nan
>>> acos(1+x).series(x)
nan
>>> acos(1-x*x).series(x)
nan
>>> acos(1+x*x).series(x)
nan
In other words, it was not implemented.
ness01/905_series branch:
>>> acos(1-x).series(x)
PoleError: Cannot expand acos(1 - x) around 0
Right with remarks, that Taylor series do not exists indeed, but in future
plans to obtain series of another kind. And now even several examples of it
are implemented in SymPy, e.g. `sqrt(sin(x))`
>>> acos(1+x).series(x)
(oo)*I*x + (oo)*I*x**2 + (oo)*I*x**3 + (oo)*I*x**4 + (oo)*I*x**5 +
O(x**6)
Incorrect.
>>> acos(1-x*x).series(x)
x*2**(1/2) + 2**(1/2)*x**3/12 + 3*2**(1/2)*x**5/160 + O(x**6)
Compare with [1]
>>> acos(1+x*x).series(x)
I*x*2**(1/2) + (oo)*I*x**2 + (oo)*I*x**3 + (oo)*I*x**4 + (oo)*I*x**5 +
O(x**6)
Incorrect.
It is now only for information now.
Also it related with issue 564.
Formally, this issue about maximum recursion depth exceeded, and it is
solved.
But I have not more detailed opinion right now.
Also I have opinion that all issues with series are seemed to be not
EasyToFix indeed.
Addition info from Wolfram Mathematica:
[1] http://www.wolframalpha.com/input/?i=series%28acos%281-x%5E2%29%29
[2] http://www.wolframalpha.com/input/?i=series%28acos%281-x%29%29
[3] http://www.wolframalpha.com/input/?i=series%28acos%281%2Bx%29%29
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