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://support.nag.com/numeric/nl/nagdoc_30.2/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