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
1. Verfasser: HENRICI, P
Format: Artikel
Sprache:eng
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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.
ISSN:0036-1410
1095-7154
DOI:10.1137/0518108