Re: Bug with Hypergeometric2F1?

*To*: mathgroup at smc.vnet.net*Subject*: [mg99400] Re: [mg99384] Bug with Hypergeometric2F1?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 5 May 2009 05:39:32 -0400 (EDT)*References*: <200905041002.GAA22748@smc.vnet.net>

This is just the usual machine precision problem. What happens is that your vol1 first evaluates to vol1[n_, k_] = Sum[Binomial[n, i], {i, 0, k}] 2^n - Binomial[n, k + 1]*Hypergeometric2F1[1, k - n + 1, k + 2, -1] Now, this is defined for arbitrary k, not just integers, but the expression is numerically sensitive and you can check that you need precision of about 303 (or more) in the second argument to get the "right answer": vol1[1000, 1`303] 1001. but In[21]:= vol1[1000, 1`302] Out[21]= 1.00*10^3 and with only hundred digits of precision vol1[1000, 1`100] 0.*10^204 which should make it pretty clear why you can't get a sensible answer with MachinePrecision, which only uses about 16 digits. On the other hand: Sum[Binomial[1000, i], {i, 0, 1.}] 1001 because this time Mathematica does not compute the numerically sensitive general formula but replaces your inexact (and hence nonsensical) limit in Sum by an exact one and gets the "right" answer. (I put "right" in quotation marks because actually your input clearly does not make sense and so Sum would be justified in returning any answer on the GIGO principle). Andrzej Kozlowski On 4 May 2009, at 19:02, irchans wrote: > When I run this code: > > vol1[n_, k_] = Sum[ Binomial[n, i], {i, 0, k}] > vol1[1000, 1] > vol1[1000, 1.] > > I get > > Out[1] = 1001 > > > Out[2] = 7.12935*10^288 > > > I am running Mathematica 7.0.0 on windows 2000. Does anyone else have > this problem? > >

**References**:**Bug with Hypergeometric2F1?***From:*irchans <infinitgames@yahoo.com>