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Beta function

  1. Dec 28, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫(0,1) √x/√[3]1-x

    2. Relevant equations

    [itex]\Gamma[/itex]p[itex]\Gamma[/itex]q/[itex]\Gamma[/itex]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)=[itex]\Gamma[/itex](3/2) [itex]\Gamma[/itex](2/3)/[itex]\Gamma[/itex](13/6)

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

    β(3/2,2/3)=-6√π/7
     
  2. jcsd
  3. Dec 28, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    That looks wrong.

    Can you explain what you want to calculate, how you attempt to do this and where your problem is?
     
  4. Dec 28, 2013 #3
    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.
     
  5. Dec 28, 2013 #4

    mfb

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    2016 Award

    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.
     
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