The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa

TL;DR

This paper derives an explicit analytic expression for the Laplace transform of the digamma function, extending previous research and analyzing its properties, including continuity and derivative jumps at specific points.

Contribution

It provides a new explicit formula for the Laplace transform of the digamma function, building on prior work and exploring its mathematical properties.

Findings

Laplace transform expression derived explicitly

Transform is continuous in the Laplace-variable

Derivative has a jump at a=ln 2

Abstract

We provide an analytic expression for the Laplace transform of the digamma fuction. This complements work of L. Glasser, D. Manna and O. Oloa on this question. The Laplace transform is continuous in the Laplace-variable a. The derivative admits a jump at a= ln 2.