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- Rosengren, Hjalmar, 1972, et al.
(author)
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Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
- 2003
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In: Indagationes Mathematicae. ; 14, s. 483-514
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Journal article (peer-reviewed)abstract
- Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7 summations and other identities. We also use similar methods to derive new multivariable 1-psi-1 summations. Some of our results are extended to the case of elliptic hypergeometric series.
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- Rosengren, Hjalmar, 1972, et al.
(author)
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Multidimensional matrix inversions and elliptic hypergeometric series on root systems
- 2020
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In: Symmetry, Integrability and Geometry - Methods and Applications. - 1815-0659. ; 16, s. 1-21
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Journal article (peer-reviewed)abstract
- Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. As applications, we obtain a new Ar elliptic Jackson summation, as well as several quadratic, cubic and quartic summation formulas.
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