  Application of an in-plane magnetic field to rippled graphene will make the
system be a plane with randomly distributed vector potentials. Massless Dirac
fermions carrying charges on graphene are scattered by the vector potentials
and magnetoresistance is induced proportional to the square of amplitude of
in-plane magnetic field $B_{\parallel}^2$. Recently, Lundeberg and Folk
proposed a formula showing dependence of the magnetoresistance on carrier
density, in which the coefficient of $B_{\parallel}^2$ is given by a functional
of the height-correlation function $c(r)$ of ripples. In the present paper, we
give exact and explicit expressions of the coefficient for the two cases such
that $c(r)$ is (i) exponential and (ii) Gaussian. The results are given using
well-known special functions. Numerical fitting of our solutions to
experimental data were performed. It is shown that the experimental data are
well-described by the formula for the Gaussian height-correlation of ripples in
the whole region of carrier density. The standard deviation $Z$ of ripple
height and the correlation length $R$ of ripples are evaluated, which can be
compared with direct experimental measurements.
