naginterfaces.library.specfun.airy_​ai_​complex¶

naginterfaces.library.specfun.airy_ai_complex(deriv, z, scal)[source]

airy_ai_complex returns the value of the Airy function or its derivative for complex , with an option for exponential scaling.

For full information please refer to the NAG Library document for s17dg

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/s/s17dgf.html

Parameters
derivstr, length 1

Specifies whether the function or its derivative is required.

is returned.

is returned.

zcomplex

The argument of the function.

scalstr, length 1

The scaling option.

The result is returned unscaled.

The result is returned scaled by the factor .

Returns
aicomplex

The required function or derivative value.

nzint

Indicates whether or not is set to zero due to underflow. This can only occur when .

is not set to zero.

is set to zero.

Raises
NagValueError
(errno )

On entry, has an illegal value: .

(errno )

On entry, has an illegal value: .

(errno )

No computation because too large, where .

(errno )

No computation because .

(errno )

No computation – algorithm termination condition not met.

Warns
NagAlgorithmicWarning
(errno )

Results lack precision because .

Notes

airy_ai_complex returns a value for the Airy function or its derivative , where is complex, . Optionally, the value is scaled by the factor .

The function is derived from the function CAIRY in Amos (1986). It is based on the relations , and , where is the modified Bessel function and .

For very large , argument reduction will cause total loss of accuracy, and so no computation is performed. For slightly smaller , the computation is performed but results are accurate to less than half of machine precision. If is too large, and the unscaled function is required, there is a risk of overflow and so no computation is performed. In all the above cases, a warning is given by the function.

References

NIST Digital Library of Mathematical Functions

Amos, D E, 1986, Algorithm 644: A portable package for Bessel functions of a complex argument and non-negative order, ACM Trans. Math. Software (12), 265–273