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The degenerate third Painlev'{e} equation, $u^{\prime \prime} = \frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8 \epsilon u^{2} + 2ab) + \frac{b^{2}}{u}\epsilon,b \in $, and , and the associated tau-function are studied via the Isomonodromy Deformation Method. Connection formulae for asymptotics of the general as and solution and general regular as $\tau \to \pm \infty\pm i \infty$ solution are obtained.

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