On Infinite Product Identities Generating Solutions for Series

TL;DR

This paper introduces new identities for solving fractional infinite and finite series, providing methods to generate variants and apply them to infinite product problems.

Contribution

The paper presents novel identities and a systematic approach to generate variants, enhancing techniques for solving complex series and infinite products.

Findings

New identities for fractional series solutions

Method for generating identity variants

Applications to solving infinite products

Abstract

In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for some finite series. We demonstrate a method for generation of variants of the identities based on the findings. The identities are useful for solving various infinite products.