A Real Integral Representation of the Inverse Laplace Transform

This version 3 presents a rigorous real integral formula for the inverse Laplace transform, obtained by resumming a previously introduced series representation with squared factorial coefficients through a specific Bessel-based kernel. The present integral formulation is a direct extension of the series-based approach introduced in: https://doi.org In that earlier work, the inverse Laplace transform was expressed as a power series involving squared factorials. The current contribution (Version 3) demonstrates that this series admits an exact resummation into a purely real integral over a finite cycle 0, 2π. By providing a closed-form kernel based on the Bessel function J₁, this representation avoids the infinite complex paths of the classical Bromwich–Wagner contour.