naginterfaces.library.specfun.bessel_​i0_​real

naginterfaces.library.specfun.bessel_i0_real(x)[source]

bessel_i0_real returns the value of the modified Bessel function .

For full information please refer to the NAG Library document for s18ae

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s18aef.html

Parameters
xfloat

The argument of the function.

Returns
i0float

The value of the function at .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

is too large and the function returns the approximate value of at the nearest valid argument.

Notes

bessel_i0_real evaluates an approximation to the modified Bessel function of the first kind .

Note: , so the approximation need only consider .

The function is based on three Chebyshev expansions:

For ,

For ,

For ,

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

For large , the function must fail because of the danger of overflow in calculating .

References

NIST Digital Library of Mathematical Functions