tfp.substrates.numpy.math.bessel_iv_ratio

Computes I_{v} (z) / I_{v - 1} (z) in a numerically stable way.

tfp.substrates.numpy.math.bessel_iv_ratio(
    v, z, name=None
)

Let I(v, z) be the modified bessel function of the first kind. This computes the ratio of I(v, z) / I(v - 1, z). This can be more numerically stable and faster than computing the ratio directly.

This uses a continued fraction approximation attributed to Gauss for computing this quantity in the limit where z <= v, and a continued fraction approximation attributed to Perron for z > v.

v value for which I_{v}(z) / I_{v - 1}(z) should be computed. Expect v > 0.
z value for which I_{v}(z) / I_{v - 1}(z) should be computed. Expect z > 0.
name A name for the operation (optional). Default value: None (i.e., 'bessel_iv_ratio').

I(v, z) / I(v - 1, z).

References

[1]: Walter Gautschi and Josef Slavik. On the Computation of Modified Bessel Function Ratios. http://www.jstor.com/stable/2006491