  We report computations of the short-distance and the long-distance (scaling)
contributions to the square-lattice Ising susceptibility in zero field close to
T_c. Both computations rely on the use of nonlinear partial difference
equations for the correlation functions. By summing the correlation functions,
we give an algorithm of complexity O(N^6) for the determination of the first N
series coefficients. Consequently, we have generated and analysed series of
length several hundred terms, generated in about 100 hours on an obsolete
workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the
short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2.
To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4}
singularity contains only integer powers of \tau. The presence of irrelevant
variables in the scaling function is clearly evident, with contributions of
distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being
identified.
