# Novel distributional Laplacians and a Coulomb-gauge problem

## TL;DR

This paper introduces new distributional Laplacians for specific functions and applies these results to solve a Coulomb-gauge problem involving a moving point charge.

## Contribution

It presents novel distributional Laplacians for arsinh and logarithm functions and applies them to gauge transformation calculations in electromagnetism.

## Key findings

- Derived distributional Laplacians for arsinh and logarithm functions.
- Applied these Laplacians to compute gauge transformation functions for moving charges.
- Provided a new mathematical approach to Coulomb-gauge problems.

## Abstract

Novel distributional Laplacians of an arsinh function and a related logarithm function are derived. The method used to establish the former result is employed in a calculation of the gauge transformation function for the case of a uniformly moving point charge.