hankel-transform

We 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…

claim: ∑ Formula

We consider an axisymmetric pressure distribution \(p(r, \theta)=\bar{p} H(r-l)\) (radial dependence only) and show that its angular Fourier series contains only the \(m=0\) mode. Cons…

Hankel–Bessel Ladder Identities Claim. For suitable \(f_m(r)\) and \(k>0\), ∑ Formula Here ∑ Formula.

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…