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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 050, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.050 (Mi sigma833) 		 
This article is cited in 3 scientific papers (total 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
Full-text PDF (357 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2013.050
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.
Received: October 9, 2012; in final form July 21, 2013; Published online July 26, 2013
Bibliographic databases:
Document Type: Article
MSC: 33D15; 34M40; 39A13
Language: English
Citation: Takeshi Morita, “A Connection Formula for the $q$-Confluent Hypergeometric Function”, SIGMA, 9 (2013), 050, 13 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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