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Algebraic Dilogarithm Identities

Authors:	Gordon Basil Mcintosh Richard J.

Abstract:	The Rogers L-function $L(x) = sumlimits_{n = 1}^infty {frac{{x^n }} {{n^2 }} + frac{1} {2}log x} log (1 - x)$ satisfies the functional equation $L(x) + L(y) = L(xy) + Lleft( {frac{{x(1 - y)}} {{1 - xy}}} right) + Lleft( {frac{{y(1 - x)}} {{1 - xy}}} right)$ .From this we derive several other such equations, including Euler's identity L(x)+L(1-x)=L(1) and various identities arising from summation and transformation formulas for basic hypergeometric series. We also obtain some new equations of the form $sumlimits_{k = 0}^n {c_k L(theta ^k ) = 0}$ where is algebraic and the c_k are integers.

Keywords:	dilogarithm basic hypergeometric series q-series
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