Kelvin WedgeHankel Diagonalization of the Radial Bessel OperatorWe show that the order- \(n\) Hankel transform in \(r\) diagonalizes the Bessel-type radial operator \(\mathscr{L}_n\), mapping the PDE ∑ Formula to the transformed equation…2026-01-29Mathematics
Kelvin WedgeFourier Coefficients of Quadratic Forms in $\cos \gamma$ for Steady Capillary-Gravity WavesWe factor the quadratic denominator \(a+b \cos \gamma+c \cos ^2 \gamma\) and reduce the computation of its Fourier coefficients to those of \(1 /(\cos \gamma-\lambda)\). Solving the associated…2026-01-29Fluid Mechanics
Kelvin WedgeDiagonalizing Azimuthal Mode Coupling via a Discrete Fourier TransformWe recast the azimuthal mode-coupled surface equations as a block-Toeplitz convolution in the mode index and diagonalize this coupling via a discrete Fourier transform in…2026-01-29Fluid Mechanics
Kelvin WedgeCartesian Derivatives in Azimuthal Fourier–Hankel Spaceclaim: ∑ Formula2026-01-29Fluid Mechanics
Kelvin WedgeDFT Method MainWe consider the governing equations for water waves in the context of an inviscid fluid of infinite depth. The fundamental system of equations are ∑ Formula2026-01-29Fluid Mechanics
