Summary: In a previous paper [J. Phys. A 37, No. 41, 9651–9668 (2004; Zbl 1073.82014)] we gave the Fuchsian linear differential equation satisfied by , the ‘three-particle’ contribution to the susceptibility of the isotropic square lattice Ising model. This paper gives the details of the calculations (with some useful tricks and tools) which allow one to obtain a long series in polynomial time. The method is based on series expansion in the variables that appear in the -dimensional integrals representing the -particle contribution to the isotropic square lattice Ising model susceptibility . The integration rules are straightforward due to remarkable formulae we derive for these variables.
We obtain without any numerical approximation as a fully integrated series in the variable , where , with the conventional Ising model coupling constant. We also give some perspectives and comments on these results.