Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series (Q2489159)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series |
scientific article |
Statements
Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series (English)
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16 May 2006
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The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series with the Riemann Zeta function and the Dirichlet Eta function are also considered. Finally some closely-related new questions and open problems are indicated.
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Mathieu series
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asymptotic expansions
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Mellin transforms
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Bernoulli numbers
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Bessel functions
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Dirichlet series
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Fourier transforms
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Genocchi numbers
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