DLMF:25.11.E20 (Q7694)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DLMF:25.11.E20 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{k}\Hurwitzzeta^{(k)}@{s}{a}=\frac{(\ln@@{a})^{k}}{a^{s}}\left(\frac{1}{2}+\frac{a}{s-1}\right)+k!a^{1-s}\sum_{r=0}^{k-1}\frac{(\ln@@{a})^{r}}{r!(s-1)^{k-r+1}}-\frac{s(s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k}}{(x+a)^{s+2}}\diff{x}+\frac{k(2s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k-1}}{(x+a)^{s+2}}\diff{x}-\frac{k(k-1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k-2}}{(x+a)^{s+2}}\diff{x},}
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DLMF:25.11.E20
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