  We study long-range correlation functions of the rectangular Ising lattice
with cyclic boundary conditions. Specifically, we consider the situation in
which two spins are on the same column, and at least one spin is on or near
free boundaries. The low-temperature series expansions of the correlation
functions are presented when the spin-spin couplings are the same in both
directions. The exact correlation functions can be obtained by D log Pade for
the cases with simple algebraic resultant expressions. The present results show
that as the two spins are infinitely far from each other, the correlation
function is equal to the product of the row magnetizations of the corresponding
spins as expected. In terms of low-temperature series expansions, the approach
of this m-th row correlation function to the bulk correlation function for
increasing m can be understood from the observation that the dominant terms of
their series expansions are the same successively in the above two correlation
functions. The number of these dominant terms increases monotonically as m
increases.
