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Abstract
A multidimensional integral transformation is proved which is an $SU(n)$ integral analogue of Bailey’s classical very well poised ${}_{10} \varphi _9 $ hypergeometric series transformation. By applying Cauchy’s theorem and specializing parameters, an $SU(n)$${}_{10} \varphi _9 $ hypergeometric series transformation is then deduced. An $Sp(n)$ generalization of Jackson’s very well poised ${}_8 \varphi _7 $ summation theorem is also proved.
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