Christian Krause on Sat, 22 Oct 2022 21:47:23 +0200

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binomial coefficient with negative args

the binomial coefficient in GP behaves differently than I thought for negative arguments. For instance, binomial(-2,-4) yields 0 (zero). In Wolfram Alpha the result is 3. The paper by Kronenburg states this: 


For binomial(-2,-4), the second case applies: (-1)^(-2+4) * binomial(4-1,-2+4) = binomial(3,2) = 3. This is consistent with Wolfram Alpha. They also document the same definition here.

Why does PARI/GP yield different results for binomial() with negative arguments?

Best regards,