Stieltjes constants
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In mathematics, the Stieltjes constants are the numbers γk that occur in the Laurent series expansion of the Riemann zeta function:
The Stieltjes constants can also be defined as the value of the limit
The first few values are:
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n Value 0 0.5772156649015328606065120900824024310421 1 -0.072815845483676724860586 2 -0.0096903631928723184845303 3 0.002053834420303345866160 4 0.0023253700654673000574 5 0.0007933238173010627017 6 -0.00023876934543019960986 7 -0.0005272895670577510 8 -0.00035212335380 9 -0.0000343947744 10 0.000205332814909
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The zero'th constant γ0 = γ = 0.577... is known as the Euler-Mascheroni constant.
The Riemann zeta can also be expanded as other types of series. One such expansion, in terms of the falling factorial, is given in the article on the Gauss-Kuzmin-Wirsing operator.
[edit] See also
[edit] References
- Weisstein, Eric W., Stieltjes Constants at MathWorld.
- Plouffe's inverter. Stieltjes Constants, from 0 to 78, 256 digits each
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