  Finite-size scaling functions are investigated both for the mean-square
magnetization fluctuations and for the probability distribution of the
magnetization in the one-dimensional Ising model. The scaling functions are
evaluated in the limit of the temperature going to zero (T -> 0), the size of
the system going to infinity (N -> oo) while N[1-tanh(J/k_BT)] is kept finite
(J being the nearest neighbor coupling). Exact calculations using various
boundary conditions (periodic, antiperiodic, free, block) demonstrate
explicitly how the scaling functions depend on the boundary conditions. We also
show that the block (small part of a large system) magnetization distribution
results are identical to those obtained for free boundary conditions.
