airy

Airy function.

SYNOPSIS:

double x, ai, aip, bi, bip;
int airy();
airy(x, _&ai, _&aip, _&bi, _&bip);

DESCRIPTION:

Solution of the differential equation:
y"(x) = xy.
The function returns the two independent solutions Ai, Bi and their first derivatives Ai'(x), Bi'(x).
Evaluation is by power series summation for small x, by rational minimax approximations for large x.

ACCURACY:

Error criterion is absolute when function <= 1, relative when function > 1, except * denotes relative error criterion.
For large negative x, the absolute error increases as x^1.5.
For large positive x, the relative error increases as x^1.5.

Arithmetic domain function # trials peak rms
IEEE -10, 0 Ai 10000 1.6e-15 2.7e-16
IEEE 0, 10 Ai 10000 2.3e-14* 1.8e-15*
IEEE -10, 0 Ai' 10000 4.6e-15 7.6e-16
IEEE 0, 10 Ai' 10000 1.8e-14* 1.5e-15*
IEEE -10, 10 Bi 30000 4.2e-15 5.3e-16
IEEE -10, 10 Bi' 30000 4.9e-15 7.3e-16
DEC -10, 0 Ai 5000 1.7e-16 2.8e-17
DEC 0, 10 Ai 5000 2.1e-15* 1.7e-16*
DEC -10, 0 Ai' 5000 4.7e-16 7.8e-17
DEC 0, 10 Ai' 12000 1.8e-15* 1.5e-16*
DEC -10, 10 Bi 10000 5.5e-16 6.8e-17
DEC -10, 10 Bi' 7000 5.3e-16 8.7e-17

JavaScript:

var x = 9.50313909;
var a = cephes.airy(x);

Return value: Object
Format: JSON
{
"result" : integer,
"ai" : double,
"aip" : double.
"bi" : double,
"bip" : double
}