On Solving Some Trigonometric Series
Henrik Stenlund
TL;DR
This paper introduces new series representations for specific trigonometric series, Euler's Gamma function, and the logarithm, enhancing analytical and approximation methods in mathematical analysis.
Contribution
It presents novel series expressions for sin(kx)/k^2, Euler's Gamma function, and the logarithm, advancing mathematical tools for analysis and asymptotic studies.
Findings
New series for sin(kx)/k^2 derived
Fresh representation of Euler's Gamma function in terms of Riemann's Zeta function
A new series expression for the logarithm discovered
Abstract
This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a side effect. The new series are useful both for analysis, approximations and asymptotic studies.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Advanced Mathematical Theories