naginterfaces.library.specfun.bessel_​y0_​real

naginterfaces.library.specfun.bessel_y0_real(x)[source]

bessel_y0_real returns the value of the Bessel function .

For full information please refer to the NAG Library document for s17ac

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s17acf.html

Parameters
xfloat

The argument of the function.

Returns
y0float

The value of the Bessel function .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

bessel_y0_real evaluates an approximation to the Bessel function of the second kind .

Note: is undefined for and the function will fail for such arguments.

The function is based on four Chebyshev expansions:

For ,

For ,

where ,

and

For near zero, , where denotes Euler’s constant. 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