Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\) (Q1196839)
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scientific article; zbMATH DE number 89597
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\) |
scientific article; zbMATH DE number 89597 |
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Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\) (English)
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16 January 1993
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Using ideas of J. Wimp and R. McIntosh, it is proved that Gauss's explicit evaluation of \(_ 2F_ 1(a,b;c;1)\) cannot be generalized to \(_ 2F_ 1(a,b;c;x)\), for arbitrary \(a\), \(b\), \(c\) and \(x\). A short proof of Wimp's theorem that asserts that \(_ 3F_ 2(a,b,c;d,e;1)\) cannot be expressed in closed form is also given.
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explicit evaluation
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Wimp's theorem
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closed form
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0.7839279
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0.77343905
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0.76238847
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