nag_bessel_j1 (s17afc) returns the value of the Bessel function .

nag_bessel_j1 (s17afc) evaluates an approximation to the Bessel function of the first kind .

The function is based on Chebyshev expansions.

For  near zero, . 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 Section [Further Comments]), hence the function fails. Such arguments contain insufficient information to determine the phase of oscillation of ; only the amplitude, , can be determined. The range for which this occurs is roughly related to the machine precision.

"NE_REAL_ARG_GT"

On entry, x must not be greater than : . x is too large. The function returns the amplitude of the  oscillation, .

Let  be the relative error in the argument and  be the absolute error in the result. (Since  oscillates about zero, absolute error and not relative error is significant.)

If  is somewhat larger than machine precision (e.g. if  is due to data errors etc.), then  and  are approximately related by  (provided  is also within machine bounds).

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

For very large , the above relation ceases to apply. In this region, . The amplitude  can be calculated with reasonable accuracy for all , but  cannot. If  is written as  where  is an integer and , then  is determined by  only. If ,  cannot be determined with any accuracy at all. Thus if  is greater than, or of the order of, machine precision, it is impossible to calculate the phase of  and the function must fail.

None.