Bing-Hai Lei avatar
B. H. Lei
君子欲讷于言而敏于行

hankel-transform

Articles carrying this tag.

Kelvin WedgeDerivationNegative Result

Hankel 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…

Mathematics
Kelvin WedgeDerivationNegative Result

Cartesian Derivatives in Azimuthal Fourier–Hankel Space

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

Fluid Mechanics
Kelvin WedgeDerivationNegative Result

Axisymmetric 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…

Mathematics
Kelvin WedgeDerivationNegative Result

Operator 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.

Fluid Mechanics
Kelvin WedgeReading Note

Hankel 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…

Fluid Mechanics