# A note on $G_q$-summability of formal solutions of some linear $q$-difference-differential equations

## TL;DR

This paper investigates the summability properties of formal solutions to certain linear q-difference-differential equations, enhancing previous results by providing improved conditions or methods for q-G-summability.

## Contribution

It offers new insights or methods that extend the understanding of q-G-summability for formal solutions of linear q-difference-differential equations.

## Key findings

- Improved conditions for q-G-summability.
- Extended the class of equations with summable solutions.
- Refined previous results by Tahara-Yamazawa.

## Abstract

The paper discusses the summability of formal solutions of some linear q-difference-differential equations, and improves the previous result in [Tahara-Yamazawa, Opsucula Math. 35 (2015), 713-738].