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

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arxiv 2504.05514 v1 pith:MQBQ3QKF submitted 2025-04-07 math-ph math.MP

classification math-phmath.MP
keywords expansionshyperboloidsubgroupbasisinterbasistwo-dimensionalalgebracalculated
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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.

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  1. Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIB. Non-Subgroup Basis

    math-ph 2025-06 conditional novelty 6.0 of 10

    Explicit normalized eigenfunctions, interbasis expansions, and Euclidean-plane contraction limits are derived for the semi-circular, elliptic, and hyperbolic parabolic coordinate systems on the two-sheeted hyperboloid.

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