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We present a fast method for evaluating expressions of the form u j = ∑ i = 1 , i ≠ j n α i x i - x j , for j = 1 , … , n , where αi are real numbers, and xi are points in a compact interval of R . This expression can be viewed as representing the electrostatic potential generated by charges on a line in R 3 . While fast algorithms for computing the electrostatic potential of general distributions of charges in R 3 exist, in a number of situations in computational physics it is useful to have a simple and extremely fast method for eval
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