Euler-Mascheroni constant

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English

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Etymology

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Named after mathematicians Leonhard Euler (1707—1783) and Lorenzo Mascheroni (1750—1800).

The origin of the notation γ is unclear: it may have been first used by either Euler or Mascheroni.[1] It possibly reflects the constant's connection to the gamma function.

Proper noun

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Euler-Mascheroni constant

  1. (mathematics) 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.
    • 1988, Mathematics Magazine, Volume 61, Mathematical Association of America, page 82:
      The run for , the Euler-Mascheroni constant, for instance, yielded 583 approximations with six decimals or more!
    • 2003, János Surányi, Paul Erdős, translated by Barry Guiduli, Topics in the Theory of Numbers, Springer, page 100:
      In the previous section we mentioned that we do no know, for instance, whether the Euler–Mascheroni constant or the numbers for are rational.
    • 2013, Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, Springer, page 252:
      The Euler–Mascheroni constant, , considered to be the third important mathematical constant next to and , has appeared in a variety of mathematical formulae involving series, products and integrals [] .

Usage notes

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  • Mathematically, , where represents the floor function.

Synonyms

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Translations

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References

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