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Bessel 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
Integer v:
    IEEE   -125,125   -125,125      50000      3.5e-15*   1.9e-16*