Geodesic
Connection Formula for the Jackson Integral of Type $A_n$ and Elliptic Lagrange Interpolation
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the connection problem for the Jackson integral of type $A_n$. Our connection formula implies a Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific multiple series. Introducing certain elliptic Lagrange interpolation functions, we determine the explicit form of the connection coefficients. We also use basic properties of the interpolation functions to establish an explicit determinant formula for a fundamental solution matrix of the associated system of $q$-difference equations.
Keywords: Jackson integral of type $A_n$; $q$-difference equations; Selberg integral; Slater's transformation formulas; elliptic Lagrange interpolation. 
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     author = {Masahiko Ito and Masatoshi Noumi},
     title = {Connection {Formula} for the {Jackson} {Integral} of {Type} $A_n$ and {Elliptic} {Lagrange} {Interpolation}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a76/}
}
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Masahiko Ito; Masatoshi Noumi. Connection Formula for the Jackson Integral of Type $A_n$ and Elliptic Lagrange Interpolation. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a76/

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