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Lemma 5.4 .
As z → ∞ z\rightarrow\infty
(5.43) 𝒢 k ( z ) \displaystyle\mathcal{G}_{k}(z) ∼ 1 2 π ⋅ ( λ k n ) 1 4 ⋅ e 2 λ k n ⋅ z n 2 z n − 2 4 , \displaystyle\sim\frac{1}{2\sqrt{\pi}\cdot(\frac{\lambda_{k}}{n})^{\frac{1}{4}}}\cdot\frac{e^{2\sqrt{\frac{\lambda_{k}}{n}}\cdot z^{\frac{n}{2}}}}{z^{\frac{n-2}{4}}},
(5.44) 𝒟 k ( z ) \displaystyle\mathcal{D}_{k}(z) ∼ π 2 ( λ k n ) 1 4 ⋅ e − 2 λ k n ⋅ z n 2 z n − 2 4 . \displaystyle\sim\frac{\sqrt{\pi}}{2(\frac{\lambda_{k}}{n})^{\frac{1}{4}}}\cdot\frac{e^{-2\sqrt{\frac{\lambda_{k}}{n}}\cdot z^{\frac{n}{2}}}}{z^{\frac{n-2}{4}}}.