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.Sloane, N. J. A. Sequences A096714
and A096715 in "The On-Line Encyclopedia
of Integer Sequences."
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), 
, 
, 
, 
, 
, 
, ....
