Contraction and Interbases Expansions on N-Sphere

Lie algebra contractions from o(n+1) to e(n) are used to construct the asymptotic limit of the interbasis expansions between two general subgroup chains O(n + 1) ⊃ O(n_α+n_β)⊗O(n_γ) and O(n+1) ⊃ O(n_α)⊗O(n_γ+n_β), where n+1 = n_α+n_γ+n_β. It provides the asymptotic formula of Racah coefficients for SU(2) and SU(1,1) groups.