# Definition:StieltjesConstants

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

This macro is in the category of constants.

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

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

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

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

## Bibliography

Equation (2), Section 2.21 of FI.