Infinite series of various simple functions of the logarithm include
where
is the Euler-Mascheroni constant and
is the Riemann zeta function. Note that the
first two of these are divergent in the classical sense, but converge when interpreted
as zeta-regularized sums.
See also
Logarithm,
False
Logarithmic Series,
Zeta-Regularized Sum
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References
Bromwich, T. J. I'A. and MacRobert, T. M. An
Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea,
p. 351, 1991.Hardy, G. H. Ramanujan:
Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York:
Chelsea, p. 37, 1999.Referenced on Wolfram|Alpha
Logarithmic Series
Cite this as:
Weisstein, Eric W. "Logarithmic Series."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicSeries.html
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