The log sine function, also called the logsine function, is defined by

(1)

The first few cases are given by
where
is the Riemann zeta function.
The log sine function is related to the log cosine
function by

(5)

and the two are equal if the range of integration for is restricted from 0 to to 0 to .
See also
Clausen's Integral,
Log
Cosine Function,
Log Gamma Function
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References
Boros, G. and Moll, V. "The Logsine Functions." §12.5 in Irresistible
Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals.
Cambridge, England: Cambridge University Press, pp. 202 and 245249, 2004.Referenced
on WolframAlpha
Log Sine Function
Cite this as:
Weisstein, Eric W. "Log Sine Function."
From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/LogSineFunction.html
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