# On the 2-head of the colored Jones polynomial for pretzel knots

## TL;DR

This paper derives a formula for the 2-head of the colored Jones polynomial specifically for an infinite family of pretzel knots, using skein theory and stability analysis.

## Contribution

It provides a new explicit formula for the 2-head of the colored Jones polynomial for pretzel knots, expanding understanding of their quantum invariants.

## Key findings

- Established a formula for the 2-head of the colored Jones polynomial.
- Utilized skein-theoretic techniques and stability properties.
- Focused on an infinite family of pretzel knots.

## Abstract

In this paper, we prove a formula for the 2-head of the colored Jones polynomial for an infinite family of pretzel knots. Following Hall, the proof utilizes skein-theoretic techniques and a careful examination of higher order stability properties for coefficients of the colored Jones polynomial.