Re: Another Mathematica 6 bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg86305] Re: [mg86284] Another Mathematica 6 bug?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 8 Mar 2008 05:39:56 -0500 (EST)

```They appear to be equivalent for Re[n-X] > -1/4

sol = FullSimplify[
Integrate[p*p^X*(1 - p)^(n - X)*p^(X - 1/2)*(1 - p)^(n - X - 1/2), {p, 0,
1}, GenerateConditions -> False]]

(1/2)*Pi*(4*X + 1)*
Hypergeometric2F1[-2*n,
2*X + 3/2, 2, 1]*Sec[2*Pi*X]

See http://functions.wolfram.com/07.23.03.0002.01

For the stated condition

sol2 = FullSimplify[
sol /. Hypergeometric2F1[a_, b_, c_, 1] ->

Gamma[c] Gamma[c - a - b]/(Gamma[c - a] Gamma[c - b])]

-((Pi*Gamma[2*n - 2*X + 1/2]*
Sec[2*Pi*X])/(Gamma[2*n + 2]*
Gamma[-2*X - 1/2]))

Which is equivalent to the result that you were expecting

sol2 == Gamma[1/2 + 2*n - 2*X]*Gamma[3/2 + 2*X]/Gamma[2 + 2*n] // FullSimplify

True

Bob Hanlon

---- Francogrex <franco at grex.org> wrote:
> 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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