R.K. Pathria Problem:6.10

1. Nov 19, 2012

phy07

1. The problem statement, all variables and given/known data

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. Nov 19, 2012

dextercioby

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

$$K_{\nu} (z) = \int\limits_{0}^{\infty} e^{-z\cosh t}\cosh \nu t {}{} ~ dt$$

Last edited: Nov 19, 2012
3. Nov 21, 2012

phy07

thanks for your help.now i found a result likes the modified Bessel function.
$$\int\limits_{0}^{\infty} e^{-a\cosh θ}\cosh \3 θ {}{} ~ dθ -\int\limits_{0}^{\infty} e^{-a\cosh θ}\cosh \ θ {}{} ~ dθ$$
a:constant
but i don't know how to resolve the bessel function.can you show a way?

Last edited: Nov 21, 2012
4. Nov 21, 2012

dextercioby

What do you mean by 'resolve the Bessel function' ?

5. Nov 22, 2012

phy07

ok sorry.i must write the equation in terms of bessel function.thanks for all your helps... :)