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In both aircraft bolt-hole and steam generator tube inspections, eddy current probes are utilized to scan the inner surface of the cylindrical structure for defects. A combination of integral methods and analytical approaches provide an effective means of simulating such inspections thereby quantifying their performance and providing a means of characterizing flaws. For integral methods to be successful, a knowledge of the relevant integral kernel is required but there is also a need for fast computations of the electromagnetic field. In this paper we show that by truncating the solution domain, traditional incident field calculations can be accelerated and extended to new configurations. Both the field and probe signal are expressed in the form of a double series instead of an integral and a series. The double series form provides an efficient means of evaluating the field in a finite hole or tube using analytical expressions. As an example, double-series impedance calculations for a coil whose axis is offset and parallel to that of the hole are shown to give good agreement with experiment. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]