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# Stieltjes constants

### From OeisWiki

The **Stieltjes constants** for arise from the Laurent expansion of about , where is the Riemann zeta function. There are infinitely many positive as well as negative Stieltjes constants. These constants are named after Thomas Jan Stieltjes. The Stieltjes constants are sometimes referred to as **generalized Euler constants**.

where is the Euler-Mascheroni constant.

## Contents |

## Euler-Mascheroni constant

Since

it implies that .

is the familiar Euler-Mascheroni constant usually notated just .

## Table of Stieltjes constants

(8 places) | A-number | |
---|---|---|

0
| + 0.57721566 | A001620 |

1
| − 0.07281584 | A082633 × (−1) |

2
| − 0.00969036 | A086279 × (−1) |

3
| + 0.00205383 | A086280 |

4
| + 0.00232537 | A086281 |

5
| + 0.00079332 | A086282 |

6
| − 0.00023876 | A183141 × (−1) |

7
| − 0.00052728 | A183167 × (−1) |

8
| − 0.00035212 | A183206 × (−1) |

9
| − 0.00003439 | A184853 × (−1) |

10
| + 0.00020533 | A184854 |

## Inequality

## Notes

## External links

- Weisstein, Eric W., Stieltjes Constants, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/StieltjesConstants.html]
- Mark W. Coffey, Series of zeta values, the Stieltjes constants, and a sum S_\gamma(n), 2009.
- Simon Plouffe, Stieltjes Constants from 0 to 78, to 256 digits each. Copyright: Simon Plouffe/Plouffe's Inverter (c) 1986.