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OfALargeWholeOrder(System.Numerics.Complex,System.Double)
Method (no overloads)
Summary
binomial(n, k) for a whole
k of at least a million and an
n at most half of it that is not a whole number at least 0:
(-1)^k Γ(k - n)/(Γ(k + 1) Γ(-n)), with
the logarithm of
Γ(k - n)/Γ(k + 1) by
LogGammaRatio(System.Numerics.Complex,System.Numerics.Complex,System.Double); null for any other. As a product
it took k steps, which for
binomial(-1/2, 10^12), whose factors never take it to 0, is 10^12; and past
the longs it went through the gamma function, whose two logarithms near
k ln k cancelled to their
rounding error:
binomial(-5/2, 10^20) was 1, where it is
7.52e29.
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