Differential equations of spin dynamics and asymptotic expansion of quantum expectation values near the classical limit. I

A large class of functional representations for spin operators in the spaces of the phase functions of a two-dimensional oscillator and functions on the unit sphere is constructed by means of generating functionals. The group-theoretical meaning of the formalism and its connection with the method of coherent states are discussed. Rules are found for rewriting the operator equations of motion in the form of differential equations for the functions that represent the operators.