jvBessel function of non-integer order.
double v, x, y, jv();
y = jv(v, x);
Returns a Bessel function of order v of the argument, where v is real. Negative x is allowed if v is an integer.
Several expansions are included: the ascending power series, the Hankel expansion, and two transitional expansions for large v. If v is not too large, it is reduced by recurrence to a region of best accuracy. The transitional expansions give 12D accuracy for v > 500.
Results for integer v are indicated by *, where x and v both vary from -125 to +125. Otherwise, x ranges from 0 to 125, v ranges as indicated by "domain." Error criterion is absolute, except relative when |jv()| > 1.
arithmetic v domain x domain # trials peak rms
IEEE 0,125 0,125 100000 4.6e-15 2.2e-16
IEEE -125,0 0,125 40000 5.4e-11 3.7e-13
IEEE 0,500 0,500 20000 4.4e-15 4.0e-16
IEEE -125,125 -125,125 50000 3.5e-15* 1.9e-16*