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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