TOPICS
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),
,
,
,
,
,
,
....
See also
Airy Functions, Root, ZeroExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Airy Function ZerosCite this as:
Weisstein, Eric W. "Airy Function Zeros." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AiryFunctionZeros.html