Some series whose coefficients involve the values \(\zeta\) (n) for n odd (Q1123922)
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scientific article; zbMATH DE number 4110796
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some series whose coefficients involve the values \(\zeta\) (n) for n odd |
scientific article; zbMATH DE number 4110796 |
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Some series whose coefficients involve the values \(\zeta\) (n) for n odd (English)
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1989
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The author uses two basic formulas for the digamma function \(\psi\) (z) to derive series that involve the numbers \(\zeta (2n+1)\). An example of such a series is \(\sum^{\infty}_{n=1}(-1)^{n+1}\zeta (4n-1)/4^ n=1/4.\) The series are also expressed in trigonometric form for special choices of the variable and their use in representing the solutions of the wave equation is indicated.
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digamma function
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odd arguments of Riemann-zeta function
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series representations
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trigonometric forms
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wave solutions
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