Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral involving power , exp and exp(power)

  1. Feb 4, 2012 #1
    I need some help evaluating the following integral from 0 to inifinity and a,p,c are positive reals, p>=1

    \int\limit_0^\infty\ x^{p-1}e^{-x}e^{-c x^a} dx
     
  2. jcsd
  3. Feb 4, 2012 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    In general it can be done only numerically - probably using a series expansion of e-cxa.
     
  4. Feb 5, 2012 #3
    How can use the series expansion
     
  5. Feb 5, 2012 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    After the expansion each term will be e-x times a power of x. If the powers are integers, then explicit term by term integration is possible. If they are not integers, I can't see anything but brute force numerical integration
     
  6. Feb 12, 2012 #5
    If I have a power series is the variable x which is uniformaly absolutely convergent over the entire positive Reals domain and then I multipled this series by F(x) which does not depend on the series index n. ie all the series terms are multipiled by the same fuction. Will the resulting series preserve the convergence properties?
     
  7. Feb 12, 2012 #6

    mathman

    User Avatar
    Science Advisor
    Gold Member

    It will as long as |F(x)G(x)| is integrable, where G(x) is the function represented by the power series.
     
  8. Feb 13, 2012 #7
    Plaese I need more information about this condition can you recommend me any reading material
     
  9. Feb 13, 2012 #8

    mathman

    User Avatar
    Science Advisor
    Gold Member

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integral involving power , exp and exp(power)
  1. Exp. integral (Replies: 1)

  2. Integral of exp (-1/x) (Replies: 2)

  3. Integral of exp(-x^n) (Replies: 0)

Loading...