On simplifications of certain \(q\)-multisums (Q2370832)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On simplifications of certain \(q\)-multisums |
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On simplifications of certain \(q\)-multisums (English)
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29 June 2007
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Clever use of some transformation formulas for very-well-poised \({}_{10}\phi_9\) and \({}_{11}\phi_{10}\) basic hypergeometric series leads to some remarkable identities, where double or triple sums are transformed into single sums. These identities involve both finite sums and, by taking limits, infinite sums. It is pointed out that the identities arise naturally in combinatorics.
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\(q\)-series
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basic hypergeometric series
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Rogers-Ramanujan identities
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Andrews-Gordon identities
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combinatorial identities
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