Direct quadrature of Eq(B.5) yields \zeta=e^{2\psi}=\Phi^2+\tilde{C}\Phi+B, with \{B, \tilde{C}\} being integral constants. To resume asymptotic flatness at spatial infinity, we need \lim_{\rho,z\to\infty}\Phi=0 and \lim_{\rho,z\to\infty}e^{2\psi}=1, so there should be B=1. Also, rewrite the constant \tilde{C} as -2C for mathematical convenience in subsequent calculations, and one finally obtains the characteristic relation implied by Eqs(7.a-7.e) that
