  Using an expansion method in the variables $ x_i$ that appear in the
$(n-1)$-dimensional integrals representing the $n$-particle contribution to the
Ising square lattice model susceptibility $\chi$, we generate a long series of
coefficients for the 3-particle contribution $\chi^{(3)}$, using a $ N^4$
polynomial time algorithm. We give the Fuchsian differential equation of order
seven for $\chi^{(3)}$ that reproduces all the terms of our long series. An
analysis of the properties of this Fuchsian differential equation is performed.
