Equation 18.44.17FB2622EF514

\begin{equation} \begin{aligned} H_ j(t)& =r_ jt^{r_ j}+(r_ j+1)\varepsilon _ jt^{r_ j+1}+O(t^{2r_ j}),\\ G_ j(t)& =r_ j^2t^{r_ j}+(r_ j+1)^2\varepsilon _ jt^{r_ j+1}+O(t^{2r_ j}). \end{aligned} \end{equation}