Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIA. Subgroup Basis

Abstract

Three subgroup type eigenfunctions of the Laplace-Beltrami operator on a two-dimensional two-sheeted hyperboloid are considered and all interbasis expansions between them are calculated. It is shown how the coefficients determining the expansions and the expansions themselves between subgroup basis contract from the hyperboloid to the Euclidean plane.