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The Euler–Mascheroni constant γ

The Euler–Mascheroni constant is defined as the following limit:

The Euler–Mascheroni constant appears in Mertens' third theorem and has relations to the gamma function, the zeta function and many different integrals and series.

It is yet unknown whether γ {\displaystyle \gamma } is rational or not.

The numeric value of γ {\displaystyle \gamma } is approximately 0.57721.