 Midplane tilt contribution to asymmetric drift

Reflection symmetry makes $\overline{v_R{v}_z}$ odd in height, so its value at the midplane vanishes while its derivative need not vanish. The radial Jeans equation includes this derivative in the stellar asymmetric drift. For a velocity ellipsoid locally aligned with spherical coordinates, $\overline{v_R{v}_z}\simeq ({\sigma }_R^2-{\sigma }_z^2)z/R$, and its midplane contribution is $-({\sigma }_R^2-{\sigma }_z^2)$. Dropping a mixed moment at the symmetry plane does not justify dropping its derivative.