In a Green's function \(G(x,x')\), the primed variable \(x'\) marks the source point — the location of a unit impulse — while \(x\) is the field point where the…

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We show how the spectral relation \(\partial_z \widehat{\varphi}(k, 0)=k \tanh (k h) \widehat{\varphi}(k, 0)\) implies the physical-space operator identity \(\varphi_z(\cdot, \cdot, 0)=(|D| \tanh (h|D|)) \varphi(\cdot, \cdot, 0)\), by inverse Fourier transform and the…

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…

The math is sound. The method is not. We factor the quadratic denominator \(a+b \cos \gamma+c \cos ^2 \gamma\) and reduce the computation of its Fourier coefficients to those of…