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

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

If $$ and $$, then

10.37.1 | $$ | ||