The Euler–Mascheroni constant is defined as the limiting difference between the harmonic series and the natural logarithmpic.twitter.com/9oOFgh3C4J
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Note that, even tough the limits separately diverge, when taken together they yield a finite number.
This is actually a rather deep statement, as the EM constant appears all the time in QFT renormalization
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The Euler-Mascharoni constant also arises in a rather elegant way in this wonderful integral.
It appears along side of another one of Euler's discoveries: π²/6
Macaroni with a side of π, if you will 
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