  The main objective of the present work is to extend these investigations by
computing the gravity and limb-darkening coefficients for white dwarf
atmosphere models with hydrogen, helium, or mixed compositions (types DA, DB,
and DBA).
  We computed gravity and limb-darkening coefficients for DA, DB, and DBA white
dwarfs atmosphere models, covering the transmission curves of the Sloan, UBVRI,
Kepler, TESS, and Gaia photometric systems. Specific calculations for the
HiPERCAM instrument were also carried out. For all calculations of the
limb-darkening coefficients we used the least-squares method. Concerning the
effects of tidal and rotational distortions, we also computed for the first
time the gravity-darkening coefficients $y(\lambda)$ for white dwarfs using the
same models of stellar atmospheres as in the case of limb-darkening. A more
general differential equation was introduced to derive these quantities,
including the partial derivative $\left(\partial{\ln
I_o(\lambda)}/{\partial{\ln g}}\right)_{T_{\rm eff}}$.
  Six laws were adopted to describe the specific intensity distribution:
linear, quadratic, square root, logarithmic, power-2, and a more general one
with four coefficients. The computations are presented for the chemical
compositions log[H/He] = $-$10.0 (DB), $-$2.0 (DBA) and He/H = 0 (DA), with log
g varying between 5.0 and 9.5 and effective temperatures between 3750
K-100\,000 K. For effective temperatures higher than 40\,000 K, the models were
also computed adopting nonlocal thermal equilibirum (DA). The adopted
mixing-length parameters are ML2/$\alpha = 0.8$ (DA case) and 1.25 (DB and
DBA). The results are presented in the form of 112 tables. Additional
calculations, such as for other photometric systems and/or different values of
log[H/He], $\log g,$ and T$_{\rm eff}$ can be performed upon request.
