On integral representations of \(q\)-gamma and \(q\)-beta functions (Q2504812)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On integral representations of \(q\)-gamma and \(q\)-beta functions |
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On integral representations of \(q\)-gamma and \(q\)-beta functions (English)
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28 September 2006
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Summary: We study \(q\)-integral representations of the \(q\)-gamma and the \(q\)-beta functions. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.
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\(q\)-calculus
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\(q\)-gamma function
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\(q\)-beta function
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