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Gamma Function

  1. Nov 23, 2008 #1
    1. Numerically approximate [tex]\Gamma(\frac{3}{2})[/tex]. Is it reasonable to define these as [tex](\frac{1}{2})[/tex]!?

    2. Show in the sense of question 1. that [tex](\frac{1}{2})[/tex]! = [tex]\frac{1}{2}[/tex][tex]\sqrt{\pi}[/tex] at least numerically.


    How am i supposed to attempt this numerically? given that i do not know additional identities of the gamma function...
     
  2. jcsd
  3. Nov 23, 2008 #2

    Avodyne

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    Hmm, seems like a poorly phrased question. The usual definition of the gamma function is

    [tex]\Gamma(z)=\int_0^\infty dt\,t^{z-1}e^{-t}[/tex]

    for [itex]\mathop{\rm Re}z>0[/itex]. Then it's pretty easy to show that [itex]\Gamma(n)=(n-1)![/itex] when [itex]n[/itex] is a positive integer. You could use this integral as a basis for numerical approximation, I suppose.
     
  4. Nov 23, 2008 #3

    Dick

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    The definition of the gamma function is given by an integral. What is it? You can numerically approximate an integral. I think that's what they are after.
     
  5. Nov 23, 2008 #4
    okay, if i numerically approximate by plugging in 3/2 into the gamma function, i get infinity.

    how am i supposed to use that information to arrive at the conclusion in #2?
     
  6. Nov 23, 2008 #5

    Dick

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    No, you don't get infinity. Tell us how you did.
     
  7. Nov 23, 2008 #6
    O, im sorry. I did my math incorrectly...

    after reworking the problem, using integration by parts,
    i'm stuck at
    (-t^(1/2))/(e^t)|[tex]^{infinity}_{0}tex]+(1/2) (original integral except t^-1/2)

    after further integration, isn't it an endless cycle?
     
  8. Nov 23, 2008 #7

    Dick

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    No, you aren't going to get much of anywhere integrating by parts. I thought you wanted to make a numerical approximation. Don't you just want to approximate the integral of t^(1/2)*exp(-t) from 0 to infinity?
     
  9. Nov 23, 2008 #8
    would that be a basic fnInt(y,x,0,99) command on the calc?
     
  10. Nov 24, 2008 #9

    HallsofIvy

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    What function you use on a calculator depends on the calculator!

    Are you required to do this using a specific calculator?
     
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