Ordered operator expansions and reconstruction from ordered moments

The structure of ordered expansions in powers of boson operators and of can onical operators and the dual problem of operator reconstruction from order ed moments is derived and applied to the complete Gaussian class of orderin g. In particular, the interpolation lines between normal and antinormal ord ering and between standard and antistandard ordering with Weyl symmetrical ordering in their centre are dealt with in detail. The auxiliary operators for expansions in symmetrical ordering are explicitly found in the Fock-sta te representation and in other different representations. General and speci alized formulae are derived for different ordering of powers of linear comb inations of boson and of canonical operators which involve Hermite polynomi als of operators. The link between symmetrical ordering of powers of boson operators and of canonical operators is expressed by means of Jacobi polyno mials. Some basic formulae of operator ordering and operator expansion are collected for convenient use in the appendix.