Difference between revisions of "Stieltjes constants"

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The Stieltjes constants are defined by
 
The Stieltjes constants are defined by
 
$$\gamma_n = \displaystyle\lim_{m \rightarrow \infty} \left[ \displaystyle\sum_{k=1}^m \dfrac{\log^n(k)}{k} - \dfrac{\log^{n+1}(m)}{n+1} \right]$$
 
$$\gamma_n = \displaystyle\lim_{m \rightarrow \infty} \left[ \displaystyle\sum_{k=1}^m \dfrac{\log^n(k)}{k} - \dfrac{\log^{n+1}(m)}{n+1} \right]$$
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=Properties=
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[[Laurent series of the Riemann zeta function]]<br />
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 00:53, 9 December 2016

The Stieltjes constants are defined by $$\gamma_n = \displaystyle\lim_{m \rightarrow \infty} \left[ \displaystyle\sum_{k=1}^m \dfrac{\log^n(k)}{k} - \dfrac{\log^{n+1}(m)}{n+1} \right]$$

Properties

Laurent series of the Riemann zeta function