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05901589 Boos, Hermann G\"ohmann, Frank Properties of linear integral equations related to the six-vertex model with disorder parameter. Feigin, Boris (ed.) et al., New trends in quantum integrable systems. Proceedings of the infinite analysis 09, Kyoto, Japan, 27--31, July 2009. Dedicated to Tetsuji Miwa on the occasion on his 60th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4324-36-6/hbk; 978-981-4324-37-3/ebook). 1-10 (2011). 2011 Hackensack, NJ: World Scientific EN quantum spin chains correlation functions Summary: One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter $\alpha$. For the regularized model it was shown that all static correlation functions are polynomials in only two functions. It was further shown that these two functions can be written as contour integrals involving the solutions of a certain type of linear and nonlinear integral equations. The linear integral equations depend parametrically on $\alpha$ and generalize linear integral equations known from the study of the bulk thermodynamic properties of the model. In this note we consider the generalized dressed charge and a generalized magnetization density. We express the generalized dressed charge as a linear combination of two quotients of $Q$-functions, the solutions of Baxter's $t$-$Q$-equation. With this result we give a new proof of a lemma on the asymptotics of the generalized magnetization density as a function of the spectral parameter.