The canonical form of the E circle times epsilon Jahn-Teller Hamiltonian

The E x epsilon Jahn-Teller Hamiltonian in its Bargmann-Fock representation is transformed by the Birkhoff method into a canonical form in which all regular singularities between zero and infinity have been removed. The resulting equation is of the Kummer type and identical to the previously obtained canonical form of the Rabi Hamiltonian (Szopa M and Ceulemans A 1996 J. Math. Phys. 37 5402). The isolated exact solutions of the E x beta, E x epsilon and Gamma(8)x tau(2) Jahn-Teller Hamiltonians are identified as special symmetries of the canonical form.