  This paper develops a general theory of the Fourier-Jacobi expansion of cusp
forms on the real symplectic group of degree two including generic cusp forms.
An explicit description of such expansion is available for cusp forms
generating discrete series representations, generalized principal series
representations induced from the Jacobi parabolic subgroup and principal series
representations, where we note that the latter two cases include non-spherical
representations.
  As the archimedean local ingredients we need Fourier-Jacobi type spherical
functions and Whittaker functions, whose explicit formulas are obtained by
Hirano and by Oda, Miyazaki-Oda, Niwa and Ishii respectively. To realize these
spherical functions in the Fourier-Jacobi expansion we use the spectral theory
for the Jacobi group by Berndt-Boecherer and Berndt-Schmidt, which can be
referred to as the global ingredient of our study. Based on the theory by
Berndt-Boecherer we generalize the classical Eichler-Zagier correspondence in
the representation theoretic context.
