Definition:StieltjesConstants

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The LaTeX DLMF and DRMF macro \StieltjesConstants represents the Stiltjes constants Failed to parse (unknown function "\StieltjesConstants"): {\displaystyle \StieltjesConstants{n}} .

This macro is in the category of constants.

In math mode, this macro can be called in the following way:

\StieltjesConstants{n} produces Failed to parse (unknown function "\StieltjesConstants"): {\displaystyle {\displaystyle \StieltjesConstants{n}}}

These are defined by Failed to parse (unknown function "\StieltjesConstants"): {\displaystyle {\displaystyle \StieltjesConstants{n} := \lim_{m \to \infty} \left( \sum_{k=1}^m \frac{(\ln@@{k})^n}{k} - \frac{(\ln@@{m})^{n+1}}{n+1} \right). }}

The Stieltjes constant Failed to parse (unknown function "\StieltjesConstants"): {\displaystyle \StieltjesConstants{0}=0.57721\;56649\;01532\;86...} equals Failed to parse (unknown function "\EulerConstant"): {\displaystyle \EulerConstant} the Euler-Mascheroni constant.

Bibliography

Equation (2), Section 2.21 of FI.

URL links

http://en.wikipedia.org/wiki/Stieltjes_constants

Symbols List

 : Stieltjes constants : http://drmf.wmflabs.org/wiki/Definition:StieltjesConstants
 : sum : http://drmf.wmflabs.org/wiki/Definition:sum
 : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
 : Euler's (Euler-Mascheroni) constant : http://dlmf.nist.gov/5.2#E3