Two remarkable doubly exponential series transformations of Ramanujan (Q1322376)
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scientific article; zbMATH DE number 562817
| Language | Label | Description | Also known as |
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| English | Two remarkable doubly exponential series transformations of Ramanujan |
scientific article; zbMATH DE number 562817 |
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Two remarkable doubly exponential series transformations of Ramanujan (English)
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31 October 1994
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The paper deals with two transformation formulas for double exponential series, as e.g. \[ \alpha \sum_{k=0}^ \infty \exp (-ne^{k\alpha}), \] which can be found in Ramanujan's second note book. The authors remark that the formulas there are of asymptotic nature only and give exact identities which are proven using Poisson's summation formula as the main tool.
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transformation formula
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Gamma function
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Bernoulli numbers
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double exponential series
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Poisson's summation
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