Hi, I have a problem with obtaining a correct asymptotic expansion of an expression involving BesselK functions. The following commands:

ser5 = Simplify[Series[(1 - BesselK[0, Sqrt[s]]/BesselK[1, Sqrt[s]])/Sqrt[s], {s, ?, 5}]];
ser10 = Simplify[Series[(1 - BesselK[0, Sqrt[s]]/BesselK[1, Sqrt[s]])/Sqrt[s], {s, ?, 10}]];
ser15 = Simplify[Series[(1 - BesselK[0, Sqrt[s]]/BesselK[1, Sqrt[s]])/Sqrt[s], {s, ?, 15}]];
ser20 = Simplify[Series[(1 - BesselK[0, Sqrt[s]]/BesselK[1, Sqrt[s]])/Sqrt[s], {s, ?, 20}]];

each produces an apparently different expansion (there are differences between higher order terms). I would be glad to understand why this happens, and how to obtain a correct expansion. Leslaw