The improper integrals, appearing in the course of evaluating the vector potential A and the electric field E inside a current-carrying region, are carefully examined. It is found that the integrals exist and have a well-defined meaning only when the current density function satisfies a Hölder condition. A definite and precise way of evaluating them is derived and A, E are shown to satisfy the usual inhomogeneous equations.
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John G. Fikioris (1965) studied this question.
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