Eigenfunctions of the Laplace-Beltrami Operator on Hyperboloids
  Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple self-contained proof of Laplace's integral for a Legendre function is obtained. 
Amritanshu Prasad and M. K. Vemuri