Comment #3 on issue 3703 by [email protected]: Sum of a finite power
series performs automatic reduction which is not always valid
http://code.google.com/p/sympy/issues/detail?id=3703
I'm not sure. I can't reproduce something either before pull 1904 or after.
Sympy returns a valid answer both for symbolic M:
In [7]: mysum = summation( ((-1**n)/factorial(2*n+1)) *
(x**(4*n+2)) ,(n,1,M) )
In [9]: mysum.expand()
Out[9]:
⎛ │ 4⎞
6 4⋅M ┌─ ⎜ 1 │ x ⎟
x ⋅x ⋅ ├─ ⎜ │ ──⎟
1╵ 2 ⎝M + 2, M + 5/2 │ 4 ⎠ 2 ⎛ 2⎞
────────────────────────────────── + x - sinh⎝x ⎠
(2⋅M + 3)!
and for subs:
In [14]: mysum.subs(x,1).subs(M,10).doit()
Out[14]:
┌─ ⎛ 1 │ ⎞
├─ ⎜ │ 1/4⎟
1╵ 2 ⎝12, 25/2 │ ⎠
─────────────────────── - sinh(1) + 1
25852016738884976640000
In [15]: hyperexpand(_)
Out[15]:
8951194052869927741
- ────────────────────
51090942171709440000
n.b.:
this returns "nan" (not a number), when it should return
(1^1)+(1^2)+...(1^10)=10.
According to provided equations, it shouldn't return 1^1+1^2+...=10 at
all. What it should: -1/3!-1/5!-...-1/21!.
Changing -1**n -> (-1)**n (this seems to be a typo?) also doesn't show that
something is wrong.
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