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Euler's constant
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(Definition)
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Euler's constant  is defined by
or equivalently
Euler's constant has the value
It is related to the gamma function by
It is not known whether  is rational or irrational.
References.
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"Euler's constant" is owned by akrowne.
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(view preamble)
| Other names: |
Euler-Mascheroni constant, Mascheroni constant |
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Cross-references: irrational, rational, gamma function
There are 19 references to this entry.
This is version 7 of Euler's constant, born on 2002-02-10, modified 2006-06-26.
Object id is 1883, canonical name is EulersConstant.
Accessed 16792 times total.
Classification:
| AMS MSC: | 40A25 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Approximation to limiting values ) |
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Pending Errata and Addenda
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![$\displaystyle \gamma = \lim_{n\rightarrow \infty}\; \sum_{i=1}^n \left[\frac{1}{i} - \ln \left( 1 + \frac{1}{i} \right) \right] $](http://images.planetmath.org:8080/cache/objects/1883/l2h/img3.png "$\displaystyle \gamma = \lim_{n\rightarrow \infty}\; \sum_{i=1}^n \left[\frac{1}{i} - \ln \left( 1 + \frac{1}{i} \right) \right] $")
