Functions and Analysis

    

The Series Limit of Sum_k Cos(a Log K)/[k Log k]

Authors: Richard J. Mathar

The slowly converging series sum_{k>=2} cos(a log k)/[k log k] is evaluated numerically for a=1/2, 1, 3/2, ..., 4. After some initial terms, the infinite tail of the sum is replaced by the integral of the associated interpolating function, an Exponential Integral, and the "second form" of the Euler-Maclaurin corrections is derived from the analytic equations for higher order derivatives.

Comments: 7 Pages.

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Submission history

[v1] 2023-06-16 14:25:18

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