Beta function

1. Dec 28, 2013

Ikastun

1. The problem statement, all variables and given/known data

∫(0,1) √x/√[3]1-x

2. Relevant equations

$\Gamma$p$\Gamma$q/$\Gamma$p+q

3. The attempt at a solution

p-1=1/2 →p=3/2
q-1=-1/3 →q=2/3

β(3/2,2/3)=$\Gamma$(3/2) $\Gamma$(2/3)/$\Gamma$(13/6)

$\Gamma$3/2=1/2$\Gamma$(1/2)=√π/2
$\Gamma$2/3=-1/3
$\Gamma$13/6=7/6 1/6=7/36

β(3/2,2/3)=-6√π/7

2. Dec 28, 2013

Staff: Mentor

That looks wrong.

Can you explain what you want to calculate, how you attempt to do this and where your problem is?

3. Dec 28, 2013

Ikastun

Hello and thank you for answering.

My problem begins with the part you quote. I don't know how to properly use the recursive formula in those cases.
Regarding my attempt to calculate the integral, what I wrote above is everything.

4. Dec 28, 2013

Staff: Mentor

$\Gamma(\frac{13}{6})=\frac{7}{6}\Gamma(\frac{7}{6}) =\frac{7}{36}\Gamma(\frac{1}{6})$
For some values, an analytic expression is known, in general this doesn't work and you have to live with the expressions (or find a numerical approximation).

There is some connections between the formulas that you could explain.