The series limit of sum k 1-k log k log log k^2 - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: The slowly converging series sum {k=3}^infinity 1-k * log k * log log k^ais evaluated to 38.4067680928 at a=2. After some initial terms, the infinitetail of the sum is replaced by the integral of the associated interpolatingfunction, which is available in simple analytic form. Biases that originatefrom the difference between the smooth area under the function and thecorresponding Riemann sum are corrected by standard means. The cases a=3 anda=4 are computed in the same manner.



Author: Richard J. Mathar

Source: https://arxiv.org/







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