nag_bessel_k1 (s18adc) returns the value of the modified Bessel function, .

nag_bessel_k1 (s18adc) evaluates an approximation to the modified Bessel function of the second kind, .

The function is based on Chebyshev expansions.

For  near zero, . For very small  on some machines, it is impossible to calculate  without overflow and the function must fail.

"NE_REAL_ARG_LE"

On entry, x must not be less than or equal to 0.0: .  is undefined and the function returns zero.

"NE_REAL_ARG_TOO_SMALL"

On entry, x must be greater than : . x is too small, there is a danger of overflow and the function returns approximately the largest representable value.

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 the 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 the relative error. Eventually , which is asymptotically given by , becomes so small that it cannot be calculated without underflow and hence the function will return zero. Note that for large  the errors will be dominated by those of the math library function exp.

None.