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!

R.K. Pathria Problem:6.10

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data
    g2kqg.png
    This is my homework. I couldn't solve the integral.



    2. Relevant equations
    Kv(z) being a modified Bessel function.
    β=1/kT
    k: Boltzmann Constant


    3. The attempt at a solution
    I made p=m c sinh θ transformation and obtained an integral form as follows

    ∫exp(-mc2coshθ/kT)(cosh2θ-1)coshθ dθ

    but i couldn't forward more.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 19, 2012 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    You should use the integral representation of the modified Bessel function K as given by

    [tex] K_{\nu} (z) = \int\limits_{0}^{\infty} e^{-z\cosh t}\cosh \nu t {}{} ~ dt [/tex]
     
    Last edited: Nov 19, 2012
  4. Nov 21, 2012 #3
    thanks for your help.now i found a result likes the modified Bessel function.
    [tex]\int\limits_{0}^{\infty} e^{-a\cosh θ}\cosh \3 θ {}{} ~ dθ -\int\limits_{0}^{\infty} e^{-a\cosh θ}\cosh \ θ {}{} ~ dθ[/tex]
    a:constant
    but i don't know how to resolve the bessel function.can you show a way?
     
    Last edited: Nov 21, 2012
  5. Nov 21, 2012 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    What do you mean by 'resolve the Bessel function' ?
     
  6. Nov 22, 2012 #5
    ok sorry.i must write the equation in terms of bessel function.thanks for all your helps... :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: R.K. Pathria Problem:6.10
  1. Pathria 3.14 (Replies: 2)

  2. Pathria 7.4 (Replies: 0)

  3. Pathria 7.4 (Replies: 2)

  4. Fermi gas in Pathria (Replies: 0)

Loading...