Euler's constant - Euler's constant

Japanese: オイラーの定数 - オイラーのていすう（英語表記）Euler's constant

The series S _n = 1 + 1/2 + 1/3 + ... + 1/ n diverges as n increases, but c _n = S _n - log n converges to a limit value c as n becomes infinitesimally large. This limit value c is Euler's constant, and its value is c = 0.57721566.... The properties of this constant are difficult to understand, and it is also difficult to calculate; currently it has been calculated to more than 20,000 decimal points, but it is not even clear whether it is a rational or irrational number.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

級数 S_n＝1＋1/2＋1/3＋…＋1/n は，n が増せば発散するが c_n＝S_n－ log n は，n が限りなく大きくなるとき，極限値 c に収束する。この極限値 c がオイラーの定数で，値は，c＝0.57721566… である。この定数は，その性質がわかりにくく，また計算もしにくくて，現在小数点以下2万桁余りが計算されているが，有理数か無理数かすらもわかっていない。

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