# On a pair of identities from Ramanujan's lost notebook

## TL;DR

This paper explores new identities inspired by Ramanujan's lost notebook, deriving infinite families of Rogers-Ramanujan type identities and general partition identities, expanding the understanding of these mathematical structures.

## Contribution

The paper introduces new identities inspired by Ramanujan's work, leading to infinite families of Rogers-Ramanujan type identities and novel partition identities.

## Key findings

- Derived new identities from Ramanujan's series-product identities.
- Established infinite families of Rogers-Ramanujan type identities.
- Connected identities to general partition theory.

## Abstract

Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type identities, some of which are well-known identities from the literature. We also use these identities to derive some general identities for integer partitions.