Sums associated with the zeta function (Q1353545)
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scientific article; zbMATH DE number 1005574
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sums associated with the zeta function |
scientific article; zbMATH DE number 1005574 |
Statements
Sums associated with the zeta function (English)
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13 August 1997
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A large number of series containing the values of \(\zeta(s)\) at positive integers is evaluated. A sample example of the authors' results is \[ \sum_{k=1}^\infty {\zeta(2k)-1\over k(2k+1)4^k} = \log\left({27\pi\over4} \right) - 3. \] Proofs involve manipulations of various series and integrals involving e.g. the classical gamma-function and the so-called double gamma-function of Barnes.
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Riemann zeta-function
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gamma-function
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double gamma-function
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values at positive integers
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