naginterfaces.library.specfun.airy_​bi_​deriv

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

airy_bi_deriv returns a value for the derivative of the Airy function .

For full information please refer to the NAG Library document for s17ak

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17akf.html

Parameters
xfloat

The argument of the function.

Returns
bidfloat

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_bi_deriv calculates an approximate value for the derivative of the Airy function . It is based on a number of Chebyshev expansions.

For ,

where , and and are expansions in the 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 saves time and avoids possible underflows in calculation.

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

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

References

NIST Digital Library of Mathematical Functions