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Reviewing the Helmholtz Equation on Euclidean Plane and Interbasis Expansions

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arxiv 2504.01971 v1 pith:2IBERXM6 submitted 2025-03-24 math.CA math-phmath.MP

G.S. Pogosyan , A. Yakhno This is my paper · ORCID
classification math.CAmath-phmath.MP
keywords equationeuclideanexpansionshelmholtzinterbasisplanecoefficientscompleteness
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In the present paper we revisit the Helmholtz equation on the Euclidean plane and make some remarks on normalization constants and completeness of wave function sets. The coefficients of interbasis expansions are also reconsidered.

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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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