On Gosper-Karaji algebraic Identities

TL;DR

This paper combines algebraic and algorithmic methods, specifically Karaji's L-summing technique and Gosper's algorithm, to derive combinatorial identities from algebraic identities.

Contribution

It introduces a novel approach integrating Gosper's algorithm with L-summing to generate combinatorial identities from algebraic identities.

Findings

Unified method for deriving identities

Application to hypergeometric sums

Enhanced understanding of algebraic-combinatorial connections

Abstract

In this paper, we first quickly review the basics of an algebro-geometric method of Karaji's L-summing technique in today's modern language of algebra. Then, we also review the theory of Gosper's algorithm as a decision procedure for obtaining the indefinite sums involving hypergeometric terms. Then, we show that how one can use Gosper's algorithm equipped with the L-summing method to obtain a class of combinatorial identities associated with a given algebraic identity.