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Euler's constant, also called the Euler-Mascheroni constant and typically denoted $\gamma$, is defined to be the limiting difference between the natural logarithm and the harmonic numbers:

$$\gamma=\lim_{n \to \infty}H_n-\log n$$ where

$$H_n=1+\frac{1}{2}+\cdots+\frac{1}{n}$$

Euler's constant arises in analysis and number theory, in part due to its connections with the gamma and zeta functions.

Source: Euler-Mascheroni constant.

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