Abstract
When treating the statistics of the electric field arising from a random distribution of charged particles, in a manner analogous to earlier studies on stellar dynamics by Chandrasekhar and von Neumann, it is convenient to define a new class of functions. These functions, which are found to be generalizations of four special cases defined by the earlier authors, are examined from the viewpoint of: series expansions, differential relations, asymptotic values and normalization, roots and extrema. A practical application is briefly discussed.
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