  T. Kaluza has given a criterion for the signs of the power series of a
function that is the reciprocal of another power series. In this note the
sharpness of this condition is explored and various examples in terms of the
Gaussian hypergeometric series are given. A criterion for the monotonicity of
the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.
