(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For a relativistic ideal gas, the momentum probability distribution is given by

where [URL]http://latex.codecogs.com/gif.latex?\epsilon_p=\sqrt[]{m^2c^4+c^2p^2}.[/URL] Determine A

2. Relevant equations

3. The attempt at a solution

I know that:

[URL]http://latex.codecogs.com/gif.latex?\int_{-\infty}^{\infty}Ae^{-\frac{\epsilon_p}{k_bT}}dp=1[/URL]

Which boils down to:

[URL]http://latex.codecogs.com/gif.latex?A\int_{-\infty}^{\infty}e^{-\frac{\sqrt[]{m^2c^4+c^2p^2}}{k_bT}}dp=1[/URL]

I have no idea how to integrate this function. I have tried substitution, integration by parts...everything. After researching on line I know that the solution is:

[URL]http://upload.wikimedia.org/math/4/e/6/4e6b1c37ebe913700d63984beaa7a429.png[/URL]

But I need help understanding how a modified Bessel function pops into the solution...I don't even really understand what the Bessel function is.

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# Homework Help: How to calculate the normalization factor for relatavistic ideal gas momentum distro

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