Analogies between hadron-in-jet and dihadron fragmentation

We describe the formal analogies in the description of the inclusive production in hard processes of hadron pairs (based on dihadron fragmentation functions) and of a single hadron inside a jet (based on hadron-in-jet fragmentation functions). Since several observables involving dihadron fragmentation functions have been proposed in the past, we are able to suggest new interesting observables involving hadron-in-jet fragmentation functions, in lepton-hadron deep-inelastic scattering and hadronic collisions.