Partial reciprocal sums of the Mathieu series (Q517773)
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scientific article; zbMATH DE number 6697298
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Partial reciprocal sums of the Mathieu series |
scientific article; zbMATH DE number 6697298 |
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Partial reciprocal sums of the Mathieu series (English)
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27 March 2017
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The author proves the following double inequality for the partial sums of the Mathieu series: \[ 1/(k^2-k+ r^2+ 1/2)< \sum^\infty_{n=k} 2n/(n^2+ r^2)^2< 1/(k^2-k+r^2).\tag{1} \] As an application, he obtains the integer part of the reciprocal of the middle term of (1), for \(r\) being an integer.
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Mathieu series
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elementary method
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reciprocal sums
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