Based on the high-k Taylor expansion, you might get better convergence with f(k) = a/k^2 + b/k^(2+1/n). The coefficients tabulated in https://github.com/GalSim-developers/GalSim/issues/426#issuecomment-18855523 for integral n indicate that |a| and |b| are of the same order with a > 0 and b < 0.