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Computes I_{v} (z) / I_{v - 1} (z)
in a numerically stable way.
tfp.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.
Args | |
---|---|
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').
|
Returns | |
---|---|
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