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A new method of evaluation of Howland integrals

Chih Bing Ling, Jung Lin
1971 Mathematics of Computation  
In this paper, two Howland integrals are evaluated to 25D when the index is an odd integer. Those Howland integrals when the index is an even integer have been evaluated to 18D by Nelson. A new method of evaluation is used. The four Howland integrals were first evaluated to 5D by Howland himself, partly with Stevenson, in the papers dealing with a perforated strip [1], [2]. Ling and Nelson in an earlier paper [3] evaluated these integrals to 6D by using a different method through some
more » ... ough some intermediate integrals. Later, Ling [4] reproduced the 6D values and also added values of a group of related integrals. Recently, Nelson [5], by using the same method, evaluated the integrals to 9D. In the process of computing some related integrals arising from axisymmetrical problems, Nelson, in the same paper, further evaluated the following two Howland integrals to 18D, when k is an even integer: Jo a
doi:10.1090/s0025-5718-1971-0295537-2 fatcat:maorwpjtgrcbdgdugwo5vbcq2u