Re: Another Mathematica 6 bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg86308] Re: Another Mathematica 6 bug?
• From: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
• Date: Sat, 8 Mar 2008 05:40:29 -0500 (EST)
• References: <fqqrva\$kc2\$1@smc.vnet.net>

```If you evaluate the ratio of the two expressions you quote with random
values for n and X inserted

With[{n = RandomInteger[{0, 10}], X = RandomReal[{0, 10}]},
((1/2)*Pi*(1 + 4*X)*Hypergeometric2F1[-2*n, 3/2 + 2*X, 2, 1]*
Sec[2*Pi*X])/((Gamma[1/2 + 2*n - 2*X]*Gamma[3/2 + 2*X])/
Gamma[2 + 2*n])]

then you always get the answer 1, so (presumably) the two expressions are
equivalent. QED (more or less!).

For some unknown reason I couldn't get this ratio to symbolically simplify
to unity. It would be interesting to see how this is done.

Stephen Luttrell
West Malvern, UK

"Francogrex" <franco at grex.org> wrote in message
news:fqqrva\$kc2\$1 at smc.vnet.net...
> This integration below:
> FullSimplify[Integrate[p*p^X*(1 - p)^(n - X)*p^(X - 1/2)*
>    (1 - p)^(n - X - 1/2), {p, 0, 1}, GenerateConditions -> False]]
>
> Should give:
> (Gamma[1/2 + 2*n - 2*X]*Gamma[3/2 + 2*X])/Gamma[2 + 2*n]
>
> Instead in mathematica 6, it's giving:
> (1/2)*Pi*(4*X + 1)*Hypergeometric2F1[-2*n, 2*X + 3/2, 2,
> 1]*Sec[2*Pi*X]
>
> Something wrong?
>

```

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