On the Calculation of the Distribution Function

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Abstract
The distribution function for particles confined to a large circle is found for a repulsive potential of long range. The distribution function is calculated exactly from the Boltzmann-Gibbs equation, and compared with the solution of an implicit equation of the type used by Debye and Hückel in the theory of electrolytes. The solution of the Debye-Hückel equation agrees, for our particular potential, only fairly well with the exact distribution function.

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