This article is cited in 3 papers

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

Takeshi Morita

Graduate School of Information Science and Technology, Osaka University, 1-1 Machikaneyama-machi, Toyonaka, 560-0043, Japan

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

Keywords: $q$-Borel–Laplace transformation; $q$-difference equation; connection problem; $q$-confluent hypergeometric function.

MSC: 33D15; 34M40; 39A13

Received: October 9, 2012; in final form July 21, 2013; Published online July 26, 2013

Language: English

DOI: 10.3842/SIGMA.2013.050

Bibliographic databases:

• 
• 
• 

ArXiv: 1105.5770