# naginterfaces.library.specfun.bessel_​i1_​real_​vector¶

naginterfaces.library.specfun.bessel_i1_real_vector(x)[source]

bessel_i1_real_vector returns an array of values for the modified Bessel function .

For full information please refer to the NAG Library document for s18at

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s18atf.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. contains the approximate value of at the nearest valid argument. The threshold value is the same as for = 1 in bessel_i1_real().

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Notes

bessel_i1_real_vector evaluates an approximation to the modified 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 ,

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 cannot be represented without overflow.

References

NIST Digital Library of Mathematical Functions