In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner functions necessary to expand all phase-space functions include off-diagonal Wigner functions, which may appear technically involved. Nevertheless, it is shown here ...

In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre,...

The time t maps of Hamiltonian flows are symplectic. The order n Taylor series approximation with respect to initial conditions of such a map is symplectic through terms of order n. Given an order n Hamiltonian symplectic map, there are a variety of procedures, called symplectification methods, which produce exactly symplectic maps with Taylor series that agree with the initial Taylor map throu...