- #1
CAF123
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I have a series of dilogarithms with various arguments and I was just wondering if it is possible to tell if they are all independent or if there is a way to reduce them to a smaller minimal set?
The dilogs in question are of the form ##\text{Li}_2(X_i)##, where ##X_i## is an argument ##i=1,\dots,10## belonging to the set $$X_i \in \left\{\frac{v - u v}{1 - u v}, \frac{-1 + u v}{-u + u v}, \frac{-1 + u v}{u + u v}, \frac{-v + u v}{-u + u v},\frac{v + u v}{-1 + u v}, \frac{v + u v}{u + u v}, \frac{1 + u}{1-w}, \frac{-1 + u}{u - w}, \frac{1 + u}{u - w}, \frac{-1 + u}{u + w}\right\}$$
I have tried various transformation laws of the dilogs as described in the wolfram pages but none seem to relate the above arguments. Thanks for any comments.
The dilogs in question are of the form ##\text{Li}_2(X_i)##, where ##X_i## is an argument ##i=1,\dots,10## belonging to the set $$X_i \in \left\{\frac{v - u v}{1 - u v}, \frac{-1 + u v}{-u + u v}, \frac{-1 + u v}{u + u v}, \frac{-v + u v}{-u + u v},\frac{v + u v}{-1 + u v}, \frac{v + u v}{u + u v}, \frac{1 + u}{1-w}, \frac{-1 + u}{u - w}, \frac{1 + u}{u - w}, \frac{-1 + u}{u + w}\right\}$$
I have tried various transformation laws of the dilogs as described in the wolfram pages but none seem to relate the above arguments. Thanks for any comments.