Corollary 5.12.1 . [054C] 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
Corollary 5.12.1 .
There exists C n > 0 C_{n}>0 z ≥ 1 z\geq 1
(5.162) C n − 1 ⋅ e − j k ⋅ z n 2 ⋅ ( j k z n ) β − α \displaystyle C_{n}^{-1}\cdot e^{-\frac{j_{k}\cdot z^{n}}{2}}\cdot(j_{k}z^{n})^{\beta-\alpha} ≤ 𝒟 k ( z ) ≤ C n ⋅ e − j k ⋅ z n 2 ⋅ ( j k z n ) β − α , \displaystyle\leq\mathcal{D}_{k}(z)\leq C_{n}\cdot e^{-\frac{j_{k}\cdot z^{n}}{2}}\cdot(j_{k}z^{n})^{\beta-\alpha},
(5.163) C n − 1 ⋅ e j k ⋅ z n 2 ⋅ ( j k z n ) − β \displaystyle C_{n}^{-1}\cdot e^{\frac{j_{k}\cdot z^{n}}{2}}\cdot(j_{k}z^{n})^{-\beta} ≤ 𝒢 k ( z ) ≤ C n ⋅ e j k ⋅ z n 2 ⋅ ( j k z n ) − β . \displaystyle\leq\mathcal{G}_{k}(z)\leq C_{n}\cdot e^{\frac{j_{k}\cdot z^{n}}{2}}\cdot(j_{k}z^{n})^{-\beta}.