Airy Function Zeros
and 
have zeros on the negative real axis only. 
and 
have zeros on the negative real axis and in the sector 
. The 
th (real) roots on the negative real axis of 
, 
, 
, and 
are denoted 
, 
, 
, and 
, respectively (Abramowitz and Stegun 1972, p. 450; Fabijonas 2004; Fabijonas et al. 2004). Similarly, the 
th complex root of 
and 
in the sector 
and of 
and 
in the sector 
are denoted 
, 
, 
, and 
, respectively (Abramowitz and Stegun 1972, p. 450; Fabijonas 2004; Fabijonas et al. 2004).
The first few real roots of 
are approximately 
(OEIS A096714), 
, 
, 
, 
, 
, .... Similarly, the first few real roots of 
are approximately 
(OEIS A096715),
, 
, 
, 
, 
, 
, ....
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). "Airy Functions." §10.4 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 446-452, 1972.
Fabijonas, B. R. "Algorithm 838: Airy Functions." ACM Trans. Math. Software 30, 491-501, 2004.
Fabijonas, B. R.; Lozier, D. W.; and Olver, F. W. J. "Computation of Complex Airy Functions and Their Zeros Using Asymptotics and the Differential Equation." ACM Trans. Math. Software 30, 471-490, 2004.
Sherry, M. "The Zeros and Maxima of the Airy Function and Its First Derivative to 25 Significant Figures." Air Force Cambridge Research Center. Tech. Rep. AFCRC-TR-59-135, ASTIA AD214568. April, 1959.
