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Is anything known about the derivative of the quantum dilogarithm?

Faddeev's noncompact quantum dilogarithm is the function defined by $$ \Phi_{\mathsf b}(z) = \exp \int_{\mathbb{R} + i\varepsilon} \frac{ e^{-2i zw} }{ 4 \sinh(w \mathsf b ) \sinh(w/\...
Calvin McPhail-Snyder's user avatar