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Multivariate Quadratic Transformations and the Interpolation Kernel
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 prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the “interpolation kernel”, an analytic continuation of the author's elliptic interpolation functions which plays a major role in the proof as well as acting as the kernel for a Fourier transform on certain elliptic double affine Hecke algebras (discussed in a later paper). In the process, we give a number of examples of a new approach to proving elliptic hypergeometric integral identities, by reduction to a Zariski dense subset of a formal neighborhood of the trigonometric limit.
Keywords: quadratic transformations; elliptic special functions. 
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     author = {Eric M. Rains},
     title = {Multivariate {Quadratic} {Transformations} and the {Interpolation} {Kernel}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a18/}
}
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Eric M. Rains. Multivariate Quadratic Transformations and the Interpolation Kernel. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a18/

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