Let 
denote the Rogers L-function defined in terms
of the usual dilogarithm by
then 
satisfies the functional equation
 |
(3) |
Abel's duplication formula follows from this identity.
See also
Abel's Duplication Formula, Dilogarithm, Functional Equation, Polylogarithm, Riemann Zeta Function, Rogers L-Function
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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.
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Cite this as:
Weisstein, Eric W. "Abel's Functional Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AbelsFunctionalEquation.html