Log Sine Function

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

(1)

The first few cases are given by

			(2)
			(3)
			(4)

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.