Comment #3 on issue 2412 by [email protected]: Sketch of Sister Celine's
algorithm
http://code.google.com/p/sympy/issues/detail?id=2412
Is this still valid? If so, where we should place this helper?
BTW, it seems, that every sum from this sketch could be evaluated with the
current summation(). E.g.:
In [4]: summation((-1)**k*binomial(n,k)*binomial(2*n-2*k,n+a),(k,0,oo))
Out[4]:
⎧ ⎛ 2⋅n ⎞
⎪ ⎜ ⎟⋅Γ(-a)⋅Γ(-n + 1/2)
⎪ ⎝a + n⎠
⎪ ───────────────────────── for re(a) < 0
⎪ ⎛ a n⎞ ⎛ a n 1⎞
⎪ Γ⎜- ─ - ─⎟⋅Γ⎜- ─ - ─ + ─⎟
⎪ ⎝ 2 2⎠ ⎝ 2 2 2⎠
⎪
⎪ ∞
⎨ ____
⎪ ╲
⎪ ╲ k ⎛n⎞ ⎛-2⋅k + 2⋅n⎞
⎪ ╲ (-1) ⋅⎜ ⎟⋅⎜ ⎟
⎪ ╱ ⎝k⎠ ⎝ a + n ⎠ otherwise
⎪ ╱
⎪ ╱
⎪ ‾‾‾‾
⎪k = 0
⎩
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