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The capacitance of the circular parallel plate capacitor is calculated byexpanding the solution to the Love integral equation into a Fourier cosineseries. Previously, this kind of expansion has been carried out numerically,resulting in accuracy problems at small plate separations. We show that thisbottleneck can be alleviated, by calculating all expansion integralsanalytically in terms of the Sine and Cosine integrals. Hence, we can, in theapproximation of the kernel, use considerably larger matrices, resulting inimproved numerical accuracy for the capacitance. In order to improve theaccuracy at the smallest separations, we develop a heuristic extrapolationscheme that takes into account the convergence properties of the algorithm. Ourresults are compared with other numerical results from the literature and withthe Kirchhoff result. Error estimates are presented, from which we concludethat our results is a substantial improvement compared with earlier numericalresults.

The capacitance of the circular parallel plate capacitor obtained by solving the Love integral equation using an analytic expansion of the kernel