A Connection Formula for the q-Confluent Hypergeometric Function

A Connection Formula for the q-Confluent Hypergeometric Function

We show a connection formula for the $q$-confluent hypergeometric functions ${}_2varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2varphi_0(a,b;-;q,x)$, we obtain the connection formula for the $q$-confluent hypergeometric equation in the matrix for...

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Bibliographic Details
Main Author: Takeshi Morita
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2013-07-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
q-Borel-Laplace transformation
q-difference equation
connection problem
q-confluent hypergeometric function
Online Access:http://dx.doi.org/10.3842/SIGMA.2013.050
Description
Summary:We show a connection formula for the $q$-confluent hypergeometric functions ${}_2varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2varphi_0(a,b;-;q,x)$, 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 $qo 1^{-}$ of our connection formula.
ISSN:1815-0659

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