New distributional Laplacian identities for arsinh[a(z-b)/s] and ln[a(z-b)+sqrt(s^2+a^2(z-b)^2)] are derived and applied to solve the Coulomb-gauge Poisson equation for a uniformly moving charge.
Note on the transformation from the Lorenz gauge to the Coulomb gauge
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abstract
There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge function of this transformation that is alternative but equivalent to a formula of Jackson is derived also.
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Novel distributional Laplacians and a Coulomb-gauge problem
New distributional Laplacian identities for arsinh[a(z-b)/s] and ln[a(z-b)+sqrt(s^2+a^2(z-b)^2)] are derived and applied to solve the Coulomb-gauge Poisson equation for a uniformly moving charge.