In the case of the freely jointed chain both the angles
and
are
completely random. Then

(3.45) |

R_{g}^{2} |
= | ||

= | |||

= | (3.46) |

A simple trick exists to calculate all the moments of the chain. To this
end, look at the Fourier transform

The prime at the summation sign in the last but one line indicates that only terms with even

(3.48) |

In order to use this formula we need to know . Inverting Eq. (3.5) we get

= | |||

= | (3.49) |

Although the trick is nice, the task to evaluate the derivations is rather tedious.