  We present the first analytic scheme-independent series calculations of
anomalous dimensions of several types of baryon operators at an infrared fixed
point (IRFP) in an asymptotically free SU(3) gauge theory with $N_f$ fermions.
Separately, for an asymptotically free gauge theory with a gauge group $G$ and
$N_f$ fermions in a representation $R$ of $G$, we consider physical quantities
at an IRFP, including the anomalous dimension of gauge-invariant fermion
bilinears and the derivative of the beta function. These quantities have been
calculated in series expansions whose coefficients have been proved to be
scheme-independent at each order. We illustrate the scheme independence using a
variety of schemes, including the RI$^\prime$ scheme and several types of
momentum subtraction (MOM) schemes.
