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Karim Belabas on Sun, 23 Oct 2022 15:33:58 +0200
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Re: binomial coefficient with negative args
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- To: Christian Krause <me@ckrause.org>
- Subject: Re: binomial coefficient with negative args
- From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
- Date: Sun, 23 Oct 2022 15:32:54 +0200
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* Christian Krause [2022-10-22 21:46]:
> Hi,
> 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
> <https://arxiv.org/pdf/1105.3689.pdf> states this:
>
> [image: image.png]
>
> 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
> <https://mathworld.wolfram.com/BinomialCoefficient.html>.
>
> Why does PARI/GP yield different results for binomial() with negative
> arguments?
The extension binomial(x, k) for negative n and k was not implemented.
Just did this in the 'master' branch following Kronenburg's extension,
updating the documentation in the process.
Please test !
Cheers,
K.B.
--
Karim Belabas, IMB (UMR 5251), Université de Bordeaux
Vice-président en charge du Numérique
T: (+33) 05 40 00 29 77; http://www.math.u-bordeaux.fr/~kbelabas/
`