Some identities for spheroidal harmonics (Q807791)

Some expressions involving associated Legendre functions of first and second kind with real and imaginary arguments are considered in ellipsoidal coordinates, especially in the neighborhood of the origin in those coordinates. The basis are linear partial difference equations of second order originating from the fundamental recursion relations satisfied by Legendre functions. The explicit identities derived are useful in the study of gravitational potential work connected with ellipsoidal distributions.