naginterfaces.library.specfun.airy_​bi_​deriv_​vector

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

airy_bi_deriv_vector returns an array of values for the derivative of the Airy function .

For full information please refer to the NAG Library document for s17ax

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17axf.html

Parameters
xfloat, array-like, shape

The argument of the function, for .

Returns
ffloat, ndarray, shape

, the function values.

ivalidint, ndarray, shape

contains the error code for , for .

No error.

is too large and positive. contains zero. The threshold value is the same as for = 1 in airy_bi_deriv().

is too large and negative. contains zero. The threshold value is the same as for = 2 in airy_bi_deriv().

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Check for more information.

Notes

airy_bi_deriv_vector calculates an approximate value for the derivative of the Airy function for an array of arguments , for . 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