The Algorithm Z and Ramanujan's $_1\psi_1$ Summation

TL;DR

This paper presents a combinatorial proof of Ramanujan's $_1\psi_1$ summation formula using Zeilberger's Algorithm Z on partitions, offering a novel perspective on this classical q-series identity.

Contribution

It introduces a new combinatorial proof of Ramanujan's $_1\psi_1$ summation by applying Algorithm Z in a modified form to partitions.

Findings

Provides a combinatorial proof of Ramanujan's $_1\psi_1$ summation

Demonstrates the utility of Algorithm Z in q-series identities

Bridges partition theory with classical q-series results

Abstract

We use the Algortihm Z on partitions due to Zeilberger, in a variant form, to give a combinatorial proof of Ramanujan's $_1\psi_1$ summation formula.