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),
,
,
,
,
,
,
....
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. Software30, 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. Software30, 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.
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).
are approximately 
(OEIS A096714),
,
,
,
,
,
.... Similarly, the first few real roots of 
are approximately 
(OEIS A096715),
,
,
,
,
,
,
....
