Euler-Mascheroni constantとは 意味・読み方・使い方

固有名詞

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 ${\displaystyle \gamma }$, the Euler-Mascheroni constant, for instance, yielded 583 approximations with six decimals or more!

   • 2003, Barry Guiduli (translator), János Surányi, Paul Erdős, 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 ${\displaystyle \zeta _{2k+1}}$ for ${\displaystyle k\geq 2}$ are rational.

   • 2013, Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, Springer, page 252,

     The Euler–Mascheroni constant, ${\displaystyle \gamma }$, considered to be the third important mathematical constant next to ${\displaystyle \pi }$ and ${\displaystyle e}$, has appeared in a variety of mathematical formulae involving series, products and integrals […] .

使用する際の注意点

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

同意語

• (mathematical constant): Euler's constant, gamma

参照