Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin - Kitaev, A.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2019)
We prove that there exists a unique odd meromorphic solution of dP3, u(τ), such that u(0) = 0, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as τ→+∞.