Definition:StieltjesConstants

<< Definition:discrqHermiteII

Main Page

Definition:AffqKrawtchouk >>

The LaTeX DLMF and DRMF macro \StieltjesConstants represents the Stiltjes constants ${\displaystyle{\displaystyle\gamma_{n}}}$.

This macro is in the category of constants.

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

\StieltjesConstants{n} produces ${\displaystyle{\displaystyle{\displaystyle\gamma_{n}}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\gamma_{n}:=\lim_{m\to\infty}\left(\sum_{k=1}^{m}\frac{(\ln k)^{n}}{k}-\frac{(\ln m)^{n+1}}{n+1}\right).}}}$

The Stieltjes constant ${\displaystyle{\displaystyle\gamma_{0}=0.57721\;56649\;01532\;86...}}$ equals ${\displaystyle{\displaystyle\gamma}}$ the Euler-Mascheroni constant.

Bibliography

Equation (2), Section 2.21 of FI.

URL links

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

Symbols List

${\displaystyle{\displaystyle{\displaystyle\gamma_{n}}}}$ : Stieltjes constants : http://drmf.wmflabs.org/wiki/Definition:StieltjesConstants
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
${\displaystyle{\displaystyle{\displaystyle\gamma}}}$ : Euler's (Euler-Mascheroni) constant : http://dlmf.nist.gov/5.2#E3

<< Definition:discrqHermiteII

Main Page

Definition:AffqKrawtchouk >>