On the singularity structure of the 2D Ising model susceptibility (vol 32,pg 3889, 1999)

A remarkable product formula first derived by Palmer and Tracy (1981 Adv. A ppl. Math. 2 329) for the integrand of the two-dimensional Ising model susc eptibility expansion coefficients chi((2n)) for temperatures T less than th e critical T-c is shown to apply equally for chi((2n+1)) for T > T-c and ag rees with formulae derived by Yamada (1984 Frog. Theor. Phys. 71 1416). Thi s new representation simplifies the derivation of the results in the origin al paper of this title (1999 J. Phys. A: Math. Gen. 32 3889) to the extent that the leading series behaviour and the singularity structure can be dedu ced almost by inspection. The derivation of series is also simplified and I show, using extended series and knowledge of the singularity structure, th at there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analys is.