Hyperharmonic series involving Hurwitz zeta function (Q1048935)
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scientific article; zbMATH DE number 5655000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperharmonic series involving Hurwitz zeta function |
scientific article; zbMATH DE number 5655000 |
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Hyperharmonic series involving Hurwitz zeta function (English)
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8 January 2010
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For integers \(r\geq 1\) and \(m\geq r+1\) the authors prove that \[ \sum_{n=1}^\infty\frac{H_n^{(r)}}{n^m}=\sum_{n=1}^\infty H_n^{(r-1)}\sum_{p=0}^\infty\frac{1}{(n+p)^m}, \] where \(H_n^{(r)}\) are the hyperharmonic numbers.
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hyperharmonic numbers
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Hurwitz zeta function
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