naginterfaces.library.specfun.airy_​ai_​deriv

naginterfaces.library.specfun.airy_ai_deriv(x)[source]

airy_ai_deriv returns a value of the derivative of the Airy function .

For full information please refer to the NAG Library document for s17aj

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17ajf.html

Parameters
xfloat

The argument of the function.

Returns
aidfloat

The value of the derivative of the Airy function .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

is too large and positive. The function returns zero.

(errno )

On entry, .

Constraint: .

is too large and negative. The function returns zero.

Notes

airy_ai_deriv evaluates an approximation to the derivative of the Airy function . It is based on a number of Chebyshev expansions.

For ,

where , and and are expansions in variable .

For ,

where and are expansions in .

For ,

where is an expansion in .

For ,

where is an expansion in .

For ,

where and is an expansion in .

For the square of the machine precision, the result is set directly to . This both saves time and avoids possible intermediate underflows.

For large negative arguments, it becomes impossible to calculate a result for the oscillating function with any accuracy and so the function must fail. This occurs for , where is the machine precision.

For large positive arguments, where decays in an essentially exponential manner, there is a danger of underflow so the function must fail.

References

NIST Digital Library of Mathematical Functions