Reviewing the Helmholtz Equation on Euclidean Plane and Interbasis Expansions

2025/03/24 by Pogosyan, G. S., Yakhno, A. · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.01971

Abstract

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.

Cited by

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

Related

• Riemann-Hilbert Approach to the Helmholtz Equation in a quarter-plane. Revisited
• Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
• Polar Coordinate Solutions of the Helmholtz Equation in General Dimensions and an Orthonormal Basis
• Stable approximation of Helmholtz solutions in the 3D ball using evanescent plane waves
• Evanescent Plane Wave Approximation of Helmholtz Solutions in Spherical Domains