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

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

airy_bi_real_vector returns an array of values of the Airy function, .

For full information please refer to the NAG Library document for s17av

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17avf.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_real().

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

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_real_vector evaluates an approximation to 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 result is set directly to . This both saves time and avoids possible intermediate underflows.

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

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

References

NIST Digital Library of Mathematical Functions