The process in which neuroblasts acquire specialized structural and/or functional features that characterize the mature cerebellar Purkinje cell. Differentiation includes the processes involved in commitment of a neuroblast to a Purkinje cell fate. A Purkinje cell is an inhibitory GABAergic neuron found in the cerebellar cortex that projects to the deep cerebellar nuclei and brain stem. [ http://www.ncbi.nlm.nih.gov/pubmed/15157725 GOC:dgh GOC:cls GOC:jid http://purl.obolibrary.org/obo/go/references/0000021 GOC:dph ]