Lemma 3.27 . [050X] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Lemma 3.27 .
We have the expansion
(3.298) { w 1 = a 1 y + a 2 y 2 + O ~ ( | y | 3 ) w j = w j ′ + c j y + d j y 2 + O ~ ( | y | 3 ) , j ≥ 2 , \displaystyle\begin{cases}w_{1}=a_{1}y+a_{2}y^{2}+\widetilde{O}(|y|^{3})\\
w_{j}=w_{j}^{\prime}+c_{j}y+d_{j}y^{2}+\widetilde{O}(|y|^{3}),&j\geq 2,\end{cases}
where a 1 = | σ | − 1 > 0 a_{1}=|\sigma|^{-1}>0 a 2 a_{2} c j c_{j} d j d_{j} H H