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Algebraic Dilogarithm Identities

Authors:	Gordon Basil Mcintosh Richard J

Abstract:	The Rogers L-function $L(x) = \sum\limits_{n = 1}^\infty {\frac{{x^n }} {{n^2 }} + \frac{1} {2}\log x} \log (1 - x)$ satisfies the functional equation $L(x) + L(y) = L(xy) + L\left( {\frac{{x(1 - y)}} {{1 - xy}}} \right) + L\left( {\frac{{y(1 - x)}} {{1 - xy}}} \right)$ .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 $\sum\limits_{k = 0}^n {c_k L(\theta ^k ) = 0}$ where is algebraic and the c _k are integers.

Keywords:	dilogarithm basic hypergeometric series q-series
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