A connection formula of the $q$-confluent hypergeometric function

Details A connection formula of the $q$-confluent hypergeometric function A connection formula of the $q$-confluent hypergeometric function

2011-05-29

arxiv.org/abs/1105.5770v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We show a connection formula of the $q$-confluent hypergeometric function
${}_1\phi_1$. We introduce the $q$-Borel and $q$-Laplace transformations
following C. Zhang to obtain the connection formula. Combining with Zhang's
formula, we show a complete connection matrix for ${}_1\phi_1$. We consider the
limit $q\to 1-0$ of our connection formula.

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