# Elementary proof and application of the generating function for generalized Hall-Littlewood functions

## TL;DR

This paper introduces a generalized form of Hall-Littlewood symmetric functions via formal group laws, provides an elementary proof of their generating function, and explores some applications of this formula.

## Contribution

It presents a new generalization of Hall-Littlewood functions and offers an elementary proof of their generating function, expanding their theoretical framework.

## Key findings

- Elementary proof of the generating function formula
- New generalization of Hall-Littlewood functions
- Applications of the generating function formula

## Abstract

In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some applications of this formula.