Explicit evaluation of the q-Stokes matrices for certain confluent hypergeometric q-difference equations

2024/12/03 by Lin, Jinghong, Ma, Yiming, Xu, Xiaomeng
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.02281

Abstract

We prove a connection formula for the basic hypergeomtric function _nφ_n-1( a₁,...,a_n-1,0; b₁,...,b_n-1 ; q, z) by using the q-Borel resummation. As an application, we compute q-Stokes matrices of a special confluent hypergeometric q-difference system with an irregular singularity. We show that by letting q→ 1, the q-Stokes matrices recover the known expressions of the Stokes matrices of the corresponding confluent hypergeometric differential system.

Related

• The Stokes phenomenon for the q-difference equation satisfied by the basic hypergeometric series ₃φ₁(a₁,a₂,a₃;b₁;q,x)
• Explicit evaluation of the Stokes matrices for certain quantum confluent hypergeometric equations
• Variants of confluent q-hypergeometric equations
• Stokes matrices of hypergeometric integrals
• Stokes matrices for a class of reducible equations