Certain results involving \(q\)-series and continued fractions (Q2765935)
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scientific article; zbMATH DE number 1695202
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Certain results involving \(q\)-series and continued fractions |
scientific article; zbMATH DE number 1695202 |
Statements
2 September 2003
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basic hypergeometric function
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\(q\)-gamma function
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continued fraction expansion
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Certain results involving \(q\)-series and continued fractions (English)
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The authors find a continued fraction expansion for the basic hypergeometric function \({}_3\Phi_2\) with some special relations between the parameters, and also an expansion for a ratio of products of \(q\)-gamma functions. If one takes \(q\to 1\), these formulas yield known identities found by Ramanujan [see entries 25 and 33 of Chapter XII, Vol. 2 of Ramanujan's `Notebooks' (1957; Zbl 0138.24201)].
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