Magneto-Hall and magnetoresistance coefficients in semiconductors with mixed conductivity

Magneto-Hall and magnetoresistance formulas, correct to order $B^2$, are derived for the case in which both single-carrier and mixed-carrier effects are important. Also, a new magneto-Hall coefficient is presented: $\beta =\frac{〈{\tau }^4〉{〈\tau 〉}^2}{{〈{\tau }^2〉}^3}-1\mathrm{}$. Values of $\beta$ for various scattering mechanisms are calculated and compared with experiment.