A Connection Formula of the Hahn-Exton q-Bessel Function
Copyright policy )A Connection Formula of the Hahn-Exton q-Bessel Function
We show a connection formula of the Hahn-Exton $q$-Bessel function around the origin and the infinity. We introduce the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula. We consider the limit $p\to 1^-$ of the connection formula.
- Osaka University Japan
Hahn-Exton q-Bessel function, Difference equations, scaling (\(q\)-differences), 33D15, 34M40, 39A13, \(q\)-Borel transformation, q-Borel transformation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hahn-Exton \(q\)-Bessel function, Mathematics, Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain, connection problems
Hahn-Exton q-Bessel function, Difference equations, scaling (\(q\)-differences), 33D15, 34M40, 39A13, \(q\)-Borel transformation, q-Borel transformation, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hahn-Exton \(q\)-Bessel function, Mathematics, Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain, connection problems
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