  A generalization of the generating function for Gegenbauer polynomials is
introduced whose coefficients are given in terms of associated Legendre
functions of the second kind. We discuss how our expansion represents a
generalization of several previously derived formulae such as Heine's formula
and Heine's reciprocal square-root identity. We also show how this expansion
can be used to compute hyperspherical harmonic expansions for power-law
fundamental solutions of the polyharmonic equation.
