A Representation for the Anyon Integral Function

TL;DR

This paper introduces gamma-zeta functions that interpolate between gamma and zeta functions, providing a novel representation for the anyon integral function relevant in fractional quantum phenomena.

Contribution

The paper proposes a new pair of gamma-zeta functions that serve as a representation for the previously unavailable anyon integral function.

Findings

Gamma-zeta functions interpolate between gamma and zeta functions.

The gamma-zeta functions naturally represent the anyon integral function.

Provides a mathematical tool for studying anyons in quantum physics.

Abstract

The Fermi-Dirac and Bose-Einstein particles satisfy corresponding statistical distributions. In the phenomena of charge fractionalization and the fractional quantum Hall effect it is found that particles behave as if they are neither fermions nor bosons. Such particles are called anyons. The integral functions for bosons and fermions are available in the literature. However, there is no anyon integral function available. In this note we propose a pair of functions that interpolate, in some sense, between the gamma function and the zeta function, which we call "gamma-zeta" functions. It is pointed out that this pair of functions very naturally provides a representation of the anyon integral function.