Brillouin function

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The Brillouin function is a special function that arises in the calculation of the magnetization of compounds with magnetic moments. For net spin J, the function is given by

B_J(x) = \frac{2J + 1}{2J} \coth \left ( \frac{2J + 1}{2J} x \right )                 - {1 \over 2J} \coth \left ( {x \over 2J} \right ),

where x = \frac{g \mu_B B J}{k_B T}.

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