A technique is presented for calculating the potential integral of thin-wire theory at the singularity of the exact kernel in cases where the current is representable as piecewise constant and/or piecewise linear over an interval containing the singularity. The integral of the rapidly varying portion of the kernel is converted to a highly convergent power series. Examples of how one employs the results in computations are given.
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C.M. Butler (1975) studied this question.