airyAiDerivative¶

Evaluates the derivative of the Airy function.

Synopsis¶

airyAiDerivative (x)

Required Arguments¶

float x (Input): Argument for which the function value is desired.

Return Value¶

The derivative of the Airy function.

Description¶

The airy function \(Ai'(x)\) is defined to be the derivative of the Airy function, \(Ai(x)\). If \(x<-1.31 \varepsilon^{-2/3}\), then the answer will have no precision. If \(x<-1.31 \varepsilon^{-1/3}\), the answer will be less accurate than half precision. Here ɛ = machine(4) is the machine precision. Finally, x should be less than \(x_{max}\) so that the answer does not underflow. Very approximately, \(x_{max}=\{-1.51 \ln s\}\), where s = machine(1), the smallest representable positive number. For more information, see the description for machine.

Example¶

In this example, \(Ai'(-4.9)\) is evaluated.

from __future__ import print_function
from numpy import *
from pyimsl.math.airyAiDerivative import airyAiDerivative

x = -4.9
ans = airyAiDerivative(x)
print("Ai(-4.9) = %f" % (ans))

Output¶

Ai(-4.9) = 0.146957