nag_bessel_i1 (s18afc) returns a value for the modified Bessel function .

nag_bessel_i1 (s18afc) evaluates an approximation to the modified Bessel function of the first kind, .

The function is based on Chebyshev expansions.

For large , the function must fail because  cannot be represented without overflow.

"NE_REAL_ARG_GT"

On entry,  must not be greater than : .  is too large and the function returns the approximate value of  at the nearest valid argument.

Let  and  be the relative errors in the argument and result respectively.

If  is somewhat larger than the machine precision (i.e., if  is due to data errors etc.), then  and  are approximately related by .

However, if  is of the same order as machine precision, then rounding errors could make  slightly larger than the above relation predicts.

For small ,  and there is no amplification of errors.

For large ,  and we have strong amplification of errors. However, the function must fail for quite moderate values of  because  would overflow; hence in practice the loss of accuracy for large  is not excessive. Note that for large , the errors will be dominated by those of the math library function exp.

None.