naginterfaces.library.specfun.bessel_​j0_​real_​vector

naginterfaces.library.specfun.bessel_j0_real_vector(x)[source]

bessel_j0_real_vector returns an array of values of the Bessel function .

For full information please refer to the NAG Library document for s17as

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17asf.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.

On entry, is too large. contains the amplitude of the oscillation, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Check for more information.

Notes

bessel_j0_real_vector evaluates an approximation to the Bessel function of the first kind for an array of arguments , for .

Note: , so the approximation need only consider .

The function is based on three Chebyshev expansions:

For ,

For ,

where ,

and ,

with .

For near zero, . This approximation is used when is sufficiently small for the result to be correct to machine precision.

For very large , it becomes impossible to provide results with any reasonable accuracy (see Accuracy), hence the function fails. Such arguments contain insufficient information to determine the phase of oscillation of ; only the amplitude, , can be determined and this is returned on failure. The range for which this occurs is roughly related to machine precision; the function will fail if .

References

NIST Digital Library of Mathematical Functions

Clenshaw, C W, 1962, Chebyshev Series for Mathematical Functions, Mathematical tables, HMSO