First zeros of Ai(x):
a₁ ≈ −2.3381
a₂ ≈ −4.0879
a₃ ≈ −5.5206
a₄ ≈ −6.7867
a₅ ≈ −7.9441
aₙ ≈ −[3π(4n−1)/8]^(2/3)
Airy equation: y″ − xy = 0
Two linearly independent solutions: Ai(x) decays for x→+∞, Bi(x) grows.
WKB: For large |x|, Ai(x) ≈ (1/2√π)|x|^(−1/4) e^(−⅔x^(3/2)) for x>0
Connection to quantum tunneling at a linear potential wall.