A Cosine Integral Series Representation of the Euler-Mascheroni Constant
John M. Campbell
TL;DR
This paper derives a new series representation of the Euler-Mascheroni constant using Fourier series and integration of Knopp's series, providing a novel analytical approach.
Contribution
It introduces a cosine integral series representation of the Euler-Mascheroni constant based on Fourier analysis and integration of existing series.
Findings
New series representation of {b3} derived
Connection between Fourier series and Euler-Mascheroni constant established
Potential for improved numerical approximations of {b3}
Abstract
By integrating a series provided by Knopp, a series representation of the Euler-Mascheroni constant arises. The infinite sum representation of {\gamma} is determined through Fourier series (sawtooth wave).
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Taxonomy
TopicsOptical and Acousto-Optic Technologies · Optical Polarization and Ellipsometry