Abstract
In this paper, an infinite integral concerning numerical computation in crystallography is investigated, which was studied in two recent articles, and integration by parts is employed for calculating this typical integral. A variable transformation and a single integration by parts lead to a new formula for this integral, and at this time, it becomes a completely definite integral. Using integration by parts iteratively, the singularity at the points near three points a = 0,1,2 can be eliminated in terms containing obtained integrals, and the factors of amplifying round‐off error are released into two simple fractions independent of the integral. Series expansions for this integral are obtained, and estimations of its remainders are given, which show that accuracy 2−n is achieved in about 2n operations for every value in a given domain. Finally, numerical results are given to verify error analysis, which coincide well with the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.
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