Self-dual generalized Taub-NUT metrics (Q1911586)

\textit{T. Iwai} and \textit{N. Katayama} introduced the notion of a generalized Taub-NUT metric and showed [J. Geom. Phys. 12, No. 1, 55-75 (1993; Zbl 0851.53030)] that the self-dual metrics in this generalized family satisfy a certain ordinary differential equation. In this paper, the author solves this differential equation, thereby getting explicit expressions for all self-dual generalized Taub-NUT metrics. As an application, the author obtains the family of complete Einstein self-dual generalized Taub-NUT metrics on 4-balls, thus reproducing the Einstein self-dual metrics studied by \textit{H. Pedersen} [Math. Ann. 274, 35-59 (1986; Zbl 0566.53058)].