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Minor update to documentation.
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kmdouglass committed Jun 12, 2017
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12 changes: 10 additions & 2 deletions docs/index.rst
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Expand Up @@ -216,7 +216,7 @@ plane is calculated by taking the *sine* of a random variate

.. math::
\theta = \sqrt{\frac{-2}{a} \ln \left( 1 - X \right)}
\theta = \sqrt{ - \frac{2}{a} \ln \left( 1 - X \right)}
where :math:`X` is a random variate uniformly distributed between 0
and 1. This transformation produces random numbers with a p.d.f. for
Expand Down Expand Up @@ -244,7 +244,15 @@ is
\ell_p = \frac{1}{1 - L \left( a \right) }
where :math:`L \left( a \right)` is the `Langevin function
<https://en.wikipedia.org/wiki/Brillouin_and_Langevin_functions#Langevin_function>`_.
<https://en.wikipedia.org/wiki/Brillouin_and_Langevin_functions#Langevin_function>`_. With
the equivalence :math:`a = \ell_p`, we now have an expression for
obtaining a random number that represents the zenith angle between
segments in terms of the chain's persistence length. This is the main
result of this discussion.

.. math::
\theta = \sqrt{ - \frac{2}{\ell_p} \ln \left( 1 - X \right)}
This algorithm generates an infinitesimally thin wormlike chain
because no collision checking is performed.
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