bel's Functional Equation

Let  denote the Rogers L-function defined in terms of the usual dilogarithm by

			(1)
			(2)

then  satisfies the functional equation

(3)

Abel's duplication formula follows from this identity.

REFERENCES:

Abel, N. H. Oeuvres Completes, Vol. 2 (Ed. L. Sylow and S. Lie). New York: Johnson Reprint Corp., pp. 189-192, 1988.

Bytsko, A. G. "Two-Term Dilogarithm Identities Related to Conformal Field Theory." 9 Nov 1999. http://arxiv.org/abs/math-ph/9911012.

Gordon, B. and McIntosh, R. J. "Algebraic Dilogarithm Identities." Ramanujan J. 1, 431-448, 1997.

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 14 and 21, 1999.

Rogers, L. J. "On Function Sum Theorems Connected with the Series ." Proc. London Math. Soc. 4, 169-189, 1907.