10 Bessel FunctionsModified Bessel Functions10.36 Other Differential Equations10.38 Derivatives with Respect to Order

If $\nu $ $(\ge 0)$ is fixed, then throughout the interval $$, ${I}_{\nu}\left(x\right)$ is positive and increasing, and ${K}_{\nu}\left(x\right)$ is positive and decreasing.

If $x$ $(>0)$ is fixed, then throughout the interval $$, ${I}_{\nu}\left(x\right)$ is decreasing, and ${K}_{\nu}\left(x\right)$ is increasing.

If $$ and $|\mathrm{ph}z|\le \frac{1}{2}\pi $, then

10.37.1 | $$ | ||

Note that previously we did mention that (10.37.1) holds for $$. This is definitely not the case.