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Math Help - Beta and gamma functions

  1. #1
    Member roshanhero's Avatar
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    Beta and gamma functions

    Prove that
    Г(n+1)=nГ(n)
    I am totally confused with it,so please help me through this...........
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  2. #2
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    If \Gamma(s)=\int_0^{\infty} e^{-t}t^{s-1}dt then \Gamma(1+s)=\int_0^{\infty} e^{-t}t^s dt;\quad \text{Re}(s)>0

    I can now integrate that last integral by parts and express the results as s\Gamma(s)
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  3. #3
    Member roshanhero's Avatar
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    After that what,can I have a detail explanation here pls...............
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  4. #4
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    Quote Originally Posted by roshanhero View Post
    After that what,can I have a detail explanation here pls...............

    what are you asking? If you're asking how he got that, he used the definition of what a gamma function is.


    The last integral that he left for you to do, you need to integrate it by parts, and from the looks of it its going to take you awhile.
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  5. #5
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    Quote Originally Posted by roshanhero View Post
    After that what,can I have a detail explanation here pls...............
    Just integrate by parts the expression:

    \int_0^{\infty}e^{-t}t^{s}dt

    Just let s be an integer for now.

    Let u=e^{-t};\quad dv=t^{s}

    Now, try and finish that and you should end up with an expression that can be put into the form s\Gamma(s).
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