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Lie algebra contractions and interbasis expansions on two-dimensional hyperboloid. IIB. Non-subgroup bases
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DOI：10.1007/s40509-026-00389-8.png)
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Abstract
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The paper describes solutions of the Laplace-Beltrami equation on a two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-circular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in these coordinates through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in the specified coordinate systems from the hyperboloid to the Euclidean plane is realized.
Keywords:
Superintegrable systems
Interbasis expansions
Special functions
Lie algebra contractions
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