  We analyze the properties of the edge states of the one-dimensional Kitaev
model with long-range anisotropic pairing and tunneling. Tunneling and pairing
are assumed to decay algebraically with exponents $\alpha$ and $\beta$,
respectively, and $\alpha,\beta>1$. We determine analytically the decay of the
edges modes. We show that the decay is exponential for $\alpha=\beta$ and when
the coefficients scaling tunneling and pairing terms are equal. Otherwise, the
decay is exponential at sufficiently short distances and then algebraic at the
asymptotics. We show that the exponent of the algebraic tail is determined by
the smallest exponent between $\alpha$ and $\beta$. Our predictions are in
agreement with numerical results found by exact diagonalization and in the
literature.
