标题： 关于四面体指标和Hahn-Exton q-贝塞尔函数的一篇笔记 显示英文标题

标题： A note on the tetrahedral index and the Hahn-Exton q-Bessel function

摘要： 本文的目的是双重的：首先阐明Dimofte--Gaiotto--Gukov的$3$D指标的“基本构件”与称为四面体指标$I_\Delta (m,e)$之间的某些联系，以及Hahn--Exton的$q$类比的贝塞尔函数$J_\nu (z;q)$。 $I_\Delta$与$J_\nu$之间的对应关系将使我们能够将有用的关系从一种设置转换到另一种设置。 其次，我们想向$q$超几何社区介绍一些可能的新技术、理论和猜想，这些来自物理数学在几何拓扑学中的应用。 显示英文摘要

摘要： The purpose of this short note is twofold: First to elucidate some connections between the ``building block'' of Dimofte--Gaiotto--Gukov's $3$D index, known as the tetrahedral index $I_\Delta (m,e)$, and Hahn--Exton's $q$-analogue of the Bessel function $J_\nu (z;q)$. The correspondence between $I_\Delta$ and $J_\nu$ will allow us to translate useful relations from one setting to the other. Second, we want to introduce to the $q$-hypergeometric community some possibly new techniques, theory and conjectures arising from applications of physical mathematics to geometric topology.