# Further Results on a Function Relevant for Conformal Blocks

## TL;DR

This paper provides additional mathematical insights into the H-function relevant for conformal blocks, including recurrence relations, invariance properties, and differential operator actions, enhancing the theoretical understanding of conformal field theory calculations.

## Contribution

It explicitly proves the recurrence relation, invariance, and the action of the differential operator on the H-function, advancing the mathematical foundation of conformal blocks.

## Key findings

- Proved the recurrence relation of the H-function.
- Demonstrated the D6-invariance of the H-function.
- Validated the differential operator action on the H-function.

## Abstract

We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary quasi-primary operators. The $H$-function was introduced in a previous article and it has several interesting properties. We prove explicitly the recurrence relation as well as the $D_6$-invariance presented previously. We also demonstrate the proper action of the differential operator used to construct the $H$-function.