Re: how to get around bug
- To: mathgroup at smc.vnet.net
- Subject: [mg94410] Re: how to get around bug
- From: "gam at iap.fr" <gam at iap.fr>
- Date: Fri, 12 Dec 2008 06:54:58 -0500 (EST)
- References: <ghr0vb$8or$1@smc.vnet.net>
On Dec 11, 12:27 pm, Bob Hanlon <hanl... at cox.net> wrote:
> Since you know the workaround, define your own function.
>
> beta[z_, a_, b_, n_: 10] :=
> Module[{rz, ra, rb},
> {rz, ra, rb} = Rationalize[{z, a, b}, 0];
> N[Beta[rz, ra, rb], n]]
>
> beta[-1.7, 1.39646, -0.37188]
>
> -0.2065655322-0.6124813175 I
>
> Bob Hanlon
>
> ---- "g... at iap.fr" <g... at iap.fr> wrote:
>
> =============
> I've encountered a bug with the incomplete Beta function (both
> versions 6.0 and 7.0), which I just submitted to support.wolfram.com.
>
> Beta[-1.7, 1.39646, -0.37188]
> returns 0. + 0. i
>
> however
>
> Beta[N[-17/10, 10], N[139646/100000, 10], N[-37188/100000, 10]=
]
> provides the correct answer: -0.20657 - 0.6125 i
>
> There is a relation between Beta[z,a,b] and Hypergeometric functions
> Beta[z,a,b] = z^a/a Hypergeometric2F1[a,1-b,a+1,z] = z^a/a
> Hypergeometric1F1[1-b,a+1,z].
>
> If I estimate Hypergeometric2F1[a,1-b,a+1,z] for my values of z=-1.7,
> a=1.39646, b=-0.37188, I get
> Hypergeometric2F1[1.39646, 1.37188, 2.39646, -1.7]
> returns 0
>
> However, if I use Hypergeometric1F1[1-b,a+1,z]:
> Hypergeometric1F1[1.37188, 2.39646, -1.7]
> this returns a plausible value of 0.420134
>
> So I believe that Beta and Hypergeometric2F1 are bugged, but not
> Hypergeometric1F1.
>
> --
>
> Bob Hanlon
Thanks Bob, for your very elegant solution! Now I know about
Rationalize.
Gary