airyBiDerivative¶

Evaluates the derivative of the Airy function of the second kind.

Synopsis¶

airyBiDerivative (x)

Required Arguments¶

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

Return Value¶

The derivative of the Airy function of the second kind.

Description¶

The airy function \(Bi'(x)\) is defined to be the derivative of the Airy function of the second kind, \(Bi(x)\). 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. In addition, x should not be so large that \(\exp\left[(2/3)x^{3/2}\right]\) overflows. For more information, see the description for machine.

Example¶

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

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

x = -4.9
ans = airyBiDerivative(x)
print("Bi(-4.9) = %f" % (ans))

Output¶

Bi(-4.9) = 0.827219