iv

Modified Bessel function of noninteger order.

SYNOPSIS:

double v, x, y, iv();
y = iv(v, x);

DESCRIPTION:

Returns the modified Bessel function of order v of the argument. If x is negative, v must be integer-valued.
The function is defined as Iv(x) = Jv(ix). Here, it is computed in terms of the confluent hypergeometric function, according to the formula:
v -x
Iv(x) = (x/2) e hyperg(v+0.5, 2v+1, 2x) / gamma(v+1)

If v is a negative integer, then v is replaced by -v.

ACCURACY:

Tested at random points (v, x), with v between 0 and 30, x between 0 and 28.

Relative error:
arithmetic domain # trials peak rms
DEC 0,30 2000 3.1e-15 5.4e-16
IEEE 0,30 10000 1.7e-14 2.7e-15

Accuracy is diminished if v is near a negative integer.