Modification of Abel-Plana formula for functions with non-integrable branch-points

TL;DR

This paper presents a specific modification of the Abel-Plana formula tailored for functions with non-integrable branch-point singularities, enhancing its applicability in Casimir effect calculations.

Contribution

The authors introduce an explicit modification of the Generalized Abel-Plana formula to handle functions with non-integrable branch-point singularities.

Findings

Enables accurate Casimir calculations for functions with branch points

Provides a new mathematical tool for complex analysis in physics

Improves convergence properties of the Abel-Plana formula

Abstract

The Abel-Plana formula is a widely used tool for calculations in Casimir type problems. In this note we present a particular explicit modification of the Generalized Abel-Plana formula for the functions with non-integrable branch-point singularities.