Reduced Harmonic Representation of Partitions

TL;DR

This paper introduces a novel reduced integral representation of partitions using harmonic products, derived through hypergeometry and Fourier analysis, with a generalized theory developed via induction.

Contribution

It presents a new reduced harmonic integral representation of partitions, combining hypergeometry and Fourier series methods, and extends the theory through induction.

Findings

Derived a reduced integral representation of partitions.

Utilized hypergeometry and Fourier series in the derivation.

Generalized the theory using induction.

Abstract

In the present article the reduced integral representation of partitions in terms of harmonic products has been derived first by using hypergeometry and the new concept of fractional sum and secondly by studying the Fourier series of the kernel function appearing in the integral representation. Using the method of induction, a generalization of the theory has also been obtained.