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Math Help - integral function!

  1. #1
    Member
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    integral function!

    show that
     B(x,y)= B(x+y,3)

    i tried to solve the problem as follows

     \frac{\Gamma{x+y} \Gamma{3}}{\Gamma{x+y+3}}

    can of confuse here on how to go forward, pls i need help here.

    thanks
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  2. #2
    MHF Contributor

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    Re: integral function!

    B(x, y) is the beta function, [tex]B(x, y)= \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+ y)}, right?
    So B(x+ y, 3)= \frac{\Gamma(x+ y)\Gamma(3)}{\Gamma(x+ y+ 3)}
    (You need some parentheses to clarify what you are writing!)
    That is what you have. Now, can you use the fact \Gamma(x)= \int_0^\infty t^{x- 1}e^{-xt}dt, with some substitutions,
    to show that?
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