On Padé approximants to virial series

Padé approximants have long been used to predict virial series coefficients and to provide equations of state for low and high density materials. However, some justified criticism has appeared about this procedure. Although we agree to impose several restrictions on the use of Padé approximants, we indicate that the Padé approximant is still an excellent way to predict the first unknown virial series coefficients. As an example, we report a calculation of the $B11=128.6$ and $B12=155$ virial coefficients of the three dimensional hard sphere model that are in excellent agreement with the two most recent estimates. We also consider that the commonly used method to choose among Padé approximants is not completely reliable for this specific application and suggest an alternative new method.