The log sine function, also called the logsine function, is defined by
![S_n=int_0^pi[ln(sinx)]^ndx.](/images/equations/LogSineFunction/NumberedEquation1.svg) |
(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 245-249, 2004.Referenced
on Wolfram|Alpha
Log Sine Function
Cite this as:
Weisstein, Eric W. "Log Sine Function."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogSineFunction.html
Subject classifications
