  We derive a "master formula" for the contribution of the three-gluon
correlation function in the nucleon to the twist-3 single-spin-dependent cross
section for semi-inclusive deep-inelastic scattering, ep^\uparrow\to eDX. This
is an extension of the similar formula known for the so-called soft-gluon-pole
contribution induced by the quark-gluon correlation function in a variety of
processes. Our master formula reduces the relevant interfering partonic
subprocess with the participation of the three gluons to the Born cross
sections for the \gamma^*g\to c\bar{c} scattering, which reveals the new
structure behind the twist-3 single spin asymmetry and simplifies the actual
calculation greatly. A possible extension to higher order corrections is also
discussed.
