Let $a_i$ be the zeros of the Airy function, which is the solution top the ODE $y''-xy=0$, such that Ai(a_i)=0. According to WolframMathWorld e.g., $a_{1..4}= -2.33811, -4.08795, -5.52056, -6.7867144$.

Is there a way to obtain an asymptotic formula (as opposed to the numerical approach) for the real roots of the Airy function, for large $i$?