Status: Valid
Owner: ----
CC: [email protected]
Labels: Type-Defect Priority-Medium Simplify Concrete
New issue 3242 by [email protected]: combsimp and binomial coefficients
http://code.google.com/p/sympy/issues/detail?id=3242
In [161]: summation( binomial(n,k)**2, (k,0,oo))
Out[161]:
Γ(2⋅n + 1)
──────────
2
Γ(n + 1)
In [162]: combsimp(summation( binomial(n,k)**2, (k,0,oo)))
Out[162]:
2⋅n + 1
2 ⋅Γ(n + 1/2)
───────────────────
___
2⋅╲╱ π ⋅Γ(n + 1)
First off, I have n defined as an integer, so IMHO gamma should reduce to
factorial in that case.
Second, this is just binomial(2*n, n).
Third, why doesn't this work:
In [165]: summation( binomial(n,k)**2, (k,0,oo)).rewrite(factorial)
Out[165]:
Γ(2⋅n + 1)
──────────
2
Γ(n + 1)
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