(* loge.wl -- Central Difference Approximations of the Derivative Series[Log[1+x],{x,0,6}] d2=4/h^2*Log[1/2*delta0+Sqrt[1+1/4*delta0^2]]^2 Series[d2,{delta0,0,10}] 1440/16 d2s=(2/h*Log[1/2*delta0+Sqrt[1+1/4*delta0^2]])^(2*s) a=Series[d2s,{delta0,0,6}] a2=Expand[Normal[a]] a3=Coefficient[Coefficient[a2,(delta0/h)^(2*s)],delta0^6] Simplify[a3]