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This letter describes a method for obtaining an explicit expression for theelectrostatic energy of a charged elliptical infinitely thin disc. The chargedistribution is assumed to be polynomial. Such explicit values for this energyare fundamental for assessing the accuracy of boundary element codes. The maintools used are an extension of Copson's method and a diagonalization, given byLeppington and Levine, of the single-layer potential operator associated withthe electrostatic potential created by a distribution of charges on theelliptical disc.

Explicit computation of the electrostatic energy for an elliptical charged disc