Log Sine Function
المؤلف:
Boros, G. and Moll, V.
المصدر:
"The Logsine Functions." §12.5 in Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals. Cambridge, England: Cambridge University Press
الجزء والصفحة:
pp. 202 and 245-249
23-6-2019
2024
Log Sine Function
The log sine function, also called the logsine function, is defined by
![S_n=int_0^pi[ln(sinx)]^ndx.](http://mathworld.wolfram.com/images/equations/LogSineFunction/NumberedEquation1.gif) |
(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 
.
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.
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