Bounds for ratio of Bessel functions

Question

I know several good papers where bounds of Bessel function ration considered. For instance, the following Bessel function ratio, $$h(z) = \frac{I_{\nu}(z)}{I_{\nu+1}(z)}$$ has bounds $$h(z)<\frac{z}{\nu-1/2+\sqrt{(\nu-1/2)^2+z^2}},\quad \nu\geq 1/2,$$ $$h(z)>\frac{z}{\nu+\sqrt{\nu^2+z^2}},\quad \nu\geq 0.$$ These bounds can be obtained by fact that $h(z)$ obeys Riccati equation, $$h'(z)=1-\frac{2(\nu-1/2)}{z}h(z)-h(z)^2$$ and studying its characteristical roots. The procedure is described in this text. My question is following. Consider now the ratio $$f(z)=\frac{I_{i\nu}(z)}{I_{i\nu+1}(z)},\quad \nu\in\mathbb{R}.$$ This function obeys similar Riccati equation (with replacement $\nu\rightarrow i\nu$). As I understand, naive application of methods given in reference is not possible. So, does any (sharp) bounds for Bessel function ratio $f(z)$ can be found with help of Riccati equation?