Abstract
We obtain in exact arithmetic the order 24 linear differential operator L24 and the right-hand side E(5) of the inhomogeneous equation L24(Φ(5)) = E(5), where is a linear combination of n-particle contributions to the susceptibility of the square lattice Ising model. In Bostan et al (2009 J. Phys. A: Math. Theor. 42 275209), the operator L24 (modulo a prime) was shown to factorize into ; here we prove that no further factorization of the order 12 operator is possible. We use the exact ODE to obtain the behaviour of at the ferromagnetic critical point and to obtain a limited number of analytic continuations of beyond the principal disc defined by its high temperature series. Contrary to a speculation in Boukraa et al (2008 J. Phys. A: Math. Theor. 41 455202), we find that is singular at w = 1/2 on an infinite number of branches.
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