English

A Connection Formula for the $q$-Confluent Hypergeometric Function

Classical Analysis and ODEs 2013-07-29 v3

Abstract

We show a connection formula for the qq-confluent hypergeometric functions 2φ1(a,b;0;q,x){}_2\varphi_1(a,b;0;q,x). Combining our connection formula with Zhang's connection formula for 2φ0(a,b;;q,x){}_2\varphi_0(a,b;-;q,x), we obtain the connection formula for the qq-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit q1q\to 1^{-} of our connection formula.

Keywords

Cite

@article{arxiv.1105.5770,
  title  = {A Connection Formula for the $q$-Confluent Hypergeometric Function},
  author = {Takeshi Morita},
  journal= {arXiv preprint arXiv:1105.5770},
  year   = {2013}
}
R2 v1 2026-06-21T18:14:09.251Z