1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Write this integral in terms of gamma function

  1. Mar 17, 2015 #1
    Hey!

    So I'm self studying mary boas's mathematical methods book and I've come across this integral:

    [tex]
    \int _{0}^{\infty }e^{-x^4}dx
    [/tex]

    and I'm suppose to write this using the gamma function. The hint given states to let x^4 = u. And the answer is:

    [tex]
    \Gamma \left( \dfrac {5} {4}\right)
    [/tex]

    I tried substituting u = x^4 and du = 4x^3dx, but that doesn't give the correct answer.

    I'm a bit confused as to how the book got that answer. Any ideas would be great.

    Thanks!
     
  2. jcsd
  3. Mar 17, 2015 #2
    After substitution you should have something you can express as ## t \Gamma(t) ## which you can rewrite using the relation ## t\Gamma(t) = \Gamma(t+1)##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Write this integral in terms of gamma function
  1. Gamma Function (Replies: 8)

  2. Gamma Function (Replies: 0)

  3. Gamma Function (Replies: 18)

  4. Gamma Function (Replies: 5)

  5. Gamma function (Replies: 1)

Loading...