Proposition 5.10 . [0545] 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
Proposition 5.10 .
There exists some dimensional constant C n > 0 C_{n}>0 y ≤ − 1 y\leq-1
(5.138) e F ( t 0 ) + G ( u 0 ) ≤ C n ( − y ) γ n 2 e − y e − Q Q Q + γ n 2 . e^{F(t_{0})+G(u_{0})}\leq C_{n}(-y)^{\frac{\gamma_{n}}{2}}e^{-y}e^{-Q}Q^{Q+\frac{\gamma_{n}}{2}}.
In particular we have
(5.139) Ψ ♭ ⋅ Φ ♯ ≤ C n ⋅ Γ ( α ) Γ ( α − β ) 2 ( − y ) 1 n Q Q e − Q e y . \Tri\cdot\Ku\leq C_{n}\cdot\frac{\Gamma(\alpha)}{\Gamma(\alpha-\beta)^{2}}(-y)^{\frac{1}{n}}Q^{Q}e^{-Q}e^{y}.