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–Mascheroni constant is defined as the limiting difference between the harmonic series and the natural logarithmpic.twitter.com/9oOFgh3C4J
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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 
pic.twitter.com/itsj3nXAG0
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Just because a limit didn’t exist never stopped Euler from doing Euler
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I feel like the integral form is more illuminating. Or at least better highlights some symmetries in the equation.pic.twitter.com/iDx8T1wdP6
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I don't know anything else that Mascheroni did. I just know that when you take macaroni and you mash it you get Mascheroni.
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Leonard Susskind calls it the Euler-Macaroni constant. (Time for some pasta!)
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ثابتة أويلر-ماسكيروني الفرق بين متسلسلة واللوغاريتم الطبيعي لايزال هناك بعض غموض حول هذا الثابت ولا يزال العمل عليها.. The last expansion was in 2017 by Ron Watkins where he reached 12 digitspic.twitter.com/EMHDx5uAnc
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