Abstract: Based on the theory of the Neumann boundary value problem of geodesy on the geocentric reference ellipsoid as the boundary surface. In the Helmert space, derive the ellipsoidal series expansion of harmonic functions outside the referential ellipsoidal, the relationship of second kinds of associa-ted Legendre functions and its derivatives recurrence formula, Helmert disturbing potential and its integral kernel function with ellipsoidal harmonic formula, in order to research the Neumann boundary value problem of geodesy in the ellipsoidal coordinates.