Holomorphic extension of the de Gennes function

TL;DR

This paper proves that the de Gennes function can be extended holomorphically into a complex strip around the real axis, enhancing understanding of its analytical properties.

Contribution

It establishes the holomorphic extension of the de Gennes function, a novel result in the analysis of this mathematical object.

Findings

De Gennes function admits a holomorphic extension.

Extension is valid on a strip containing the real axis.

Results improve the understanding of the function's analytical structure.

Abstract

This note is devoted to prove that the de Gennes function has a holomorphic extension on a strip containing the real axis.