  We study jets with identified hadrons in which a family of jet-shape
variables called angularities are measured, extending the concept of
fragmenting jet functions (FJFs) to these observables. FJFs determine the
fraction of energy, z, carried by an identified hadron in a jet with
angularity, \tau_a. The FJFs are convolutions of fragmentation functions (FFs),
evolved to the jet energy scale, with perturbatively calculable matching
coefficients. Renormalization group equations are used to provide resummed
calculations with next-to-leading logarithm prime (NLL') accuracy. We apply
this formalism to two-jet events in e^+ e^- collisions with B mesons in the
jets, and three-jet events in which a J/\psi is produced in the gluon jet. In
the case of B mesons, we use a phenomenological FF extracted from e^+ e^-
collisions at the Z^0 pole evaluated at the scale \mu = m_b. For events with
J/\psi, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix
elements at the scale \mu =2 m_c. The z and \tau_a distributions from our NLL'
calculations are compared with predictions from monte carlo event generators.
While we find consistency between the predictions for B mesons and the J/\psi
distributions in \tau_a, we find the z distributions for J/\psi differ
significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs
that gives good agreement with NLL' calculations of the z distributions.
