Lie algebra contractions and interbasis expansions on two-dimensional hyperboloid. IIA. Subgroup bases

Three sets of 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. The results demonstrate how the coefficients determining the expansions and the expansions themselves between subgroup bases contract from the hyperboloid to the Euclidean plane.