Re: Inconsistent behavior?

*To*: mathgroup at smc.vnet.net*Subject*: [mg87281] Re: Inconsistent behavior?*From*: "David Park" <djmpark at comcast.net>*Date*: Sun, 6 Apr 2008 06:44:31 -0400 (EDT)*References*: <ft7ggo$bs3$1@smc.vnet.net>

Angela, Binomial is one of the functions that Mathematica knows quite a bit about. The Function help page talks about evaluation to exact results with integers and 'certain other special arguments'. Maybe Mathematica doesn't expand Binomial[n, m_Integer] when m >5 because users might prefer to keep the shorter unevaluated form in symbolic expressions. In any case, you can expand by using FunctionExpand. Binomial[n, 20] // FunctionExpand ((-19 + n) (-18 + n) (-17 + n) (-16 + n) (-15 + n) (-14 + n) (-13 + n) (-12 + n) (-11 + n) (-10 + n) (-9 + n) (-8 + n) (-7 + n) (-6 + n) (-5 + n) (-4 + n) (-3 + n) (-2 + n) (-1 + n) n)/2432902008176640000 But it is a little inconsistent to have an arbitrary break off point and not mention it. It might be more consistent to evaluate none of these cases or only m = 0 and m = 1. -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "angela" <mpopyft at lycos.com> wrote in message news:ft7ggo$bs3$1 at smc.vnet.net... > Binomial[n,4] yields > 1/24 (-3+n) (-2+n) (-1+n) n > > Binomial[n,5] yields > 1/120 (-4+n) (-3+n) (-2+n) (-1+n) n > > Binomial[n,6] yields > Binomial[n,6] > > Binomial[n,7] yields > Binomial[n,7] > > Is some setting doing this. > > Thanks; > Angela >