Comment #7 on issue 2555 by [email protected]: Wrong result from residue
http://code.google.com/p/sympy/issues/detail?id=2555
The problem is really that the series code is very messy and, apparently,
buggy. For example:
In [26]: (1/(x**2+a**2)**2).subs(x,x+I*a).series(x,n=0)
Out[26]:
1
- ─────── + O(1)
2 2
4⋅a ⋅x
In [27]: (1/(x**2+a**2)**2).subs(x,x+I*a).series(x,n=1)
Out[27]:
1
- ─────── + O(x)
2 2
4⋅a ⋅x
In [28]: (1/(x**2+a**2)**2).subs(x,x+I*a).series(x,n=2)
Out[28]:
1 ⅈ 1 ⎛ 2⎞
- ───── - ────── - ─────── + O⎝x ⎠
4 3 2 2
16⋅a 4⋅a ⋅x 4⋅a ⋅x
(For speed, all code using series tries to evaluate as few terms as
possible. However, if the big Os come out wrong, we are busted ...)
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