hankel-transform

Articles carrying this tag.

Kelvin Wedge Negative ResultsHankel Diagonalization of the Radial Bessel Operator

The math is sound. The method is not. We show that the order- \(n\) Hankel transform in \(r\) diagonalizes the Bessel-type radial operator \(\mathscr{L}_n\), mapping the PDE…

2026-01-29

Kelvin Wedge Negative ResultsCartesian Derivatives in Azimuthal Fourier–Hankel Space

The math is sound. The method is not. claim: ∑ Formula

2026-01-29

Kelvin Wedge Negative ResultsAxisymmetric Angular Fourier Modes and Hankel Transform of a Radial Heaviside Pressure Field

The math is sound. The method is not. We consider an axisymmetric pressure distribution \(p(r, \theta)=\bar{p} H(r-l)\) (radial dependence only) and show that its angular Fourier…

2026-01-29

Kelvin Wedge Negative ResultsOperator Ladder Relations for Hankel Transforms of Bessel Type

The math is sound. The method is not. Hankel–Bessel Ladder Identities Claim. For suitable \(f_m(r)\) and \(k>0\), ∑ Formula Here ∑ Formula.

2025-10-04

Kelvin Wedge Reading NotesHankel Transform of the Bi-Laplacian and an Axisymmetric Free-Surface Problem

We show how the zeroth-order Hankel transform diagonalises the radial bi-Laplacian, clarify the sign convention \(\nabla^4 \leftrightarrow k^4\), and then apply the same transform…

2025-01-11