  We generalise some well known properties of irreducible characters of finite
groups to zonal spherical functions of Gelfand pairs. This leads to a Frobenius
formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients
of its associated double-class algebra can be written in terms of zonal
spherical functions. This is a generalisation of the Frobenius formula which
writes the structure coefficients of the center of a finite group algebra in
terms of irreducible characters.
