Bessel Functions: Monotonicity and Bounds

By L. J. Landau. 2000

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Uniform Bounds for Bessel Functions (2006, background): “Landau [7] provide relatively sharp inequalities for all real x.”
Scale Invariance of the PNG Droplet and the Airy Process (2001, unknown): “′ (2t+t1/3(u′−y′2−l))/2˙ (4.17) If y<y′ and l≤ 0, the term ··· is uniformly bounded in t, land converges to 1 as t→ ∞. In fact this holds uniformly in u, u′ on compact sets. By a result of Landau [16] sup n t1/3|J n(2t)| ≤ c/21/3 (4.18) with c= 0.7857···. From the asymptotics of integer Bessel fu”