A triple product theorem for hypergeometric series
The product of three hypergeometric series of type _0 F_1 $ with arguments $x$, $\omega x$, $\omega ^2 x$ ($\omega = $third root of unity) is expressed as a single hypergeometric series of type _2 F_7 $. The proof uses differential equations; the basic idea (elimination of irreducible terms by means...
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Veröffentlicht in: | SIAM journal on mathematical analysis 1987-11, Vol.18 (6), p.1513-1518 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | The product of three hypergeometric series of type _0 F_1 $ with arguments $x$, $\omega x$, $\omega ^2 x$ ($\omega = $third root of unity) is expressed as a single hypergeometric series of type _2 F_7 $. The proof uses differential equations; the basic idea (elimination of irreducible terms by means of the Cayley-Hamilton theorem) is more generally applicable. |
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ISSN: | 0036-1410 1095-7154 |
DOI: | 10.1137/0518108 |