Euler-Mascheroni constant

English

Etymology

Named after mathematicians Template:W (1707—1783) and Template:W (1750—1800).

The origin of the notation γ is unclear: it may have been first used by either Euler or Mascheroni. It possibly reflects the constant's connection to the gamma function.

Proper noun

1. Template:Lb A constant, denoted γ and recurring in analysis and number theory, that is defined as the limiting difference between the harmonic series and the natural logarithm and has the approximate value 0.57721566.
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Usage notes

• Mathematically, $\gamma =\underset{n\to \mathrm{\infty }}{\lim }(-\ln n+{\sum }_{k=1}^n\frac{1}{k})={\int }_1^{\mathrm{\infty }}(-\frac{1}{x}+\frac{1}{\lfloor x\rfloor })dx$, where $\lfloor x\rfloor$ represents the floor function.

Synonyms

• Template:Sense Template:L, Template:L

Translations

• German: Template:T, Template:T
• Italian: Template:T