I had always wondered how the constant can be computed to high precision. I probably should have known this already, but here’s one way that it can be computed (*Gamma*, page 89):

,

where is the th Bernoulli number.

When I researching for my series of posts on conditional convergence, especially examples related to the constant , the reference *Gamma: Exploring Euler’s Constant* by Julian Havil kept popping up. Finally, I decided to splurge for the book, expecting a decent popular account of this number. After all, I’m a professional mathematician, and I took a graduate level class in analytic number theory. In short, I don’t expect to learn a whole lot when reading a popular science book other than perhaps some new pedagogical insights.

Boy, was I wrong. As I turned every page, it seemed I hit a new factoid that I had not known before.

In this series, I’d like to compile some of my favorites — while giving the book a very high recommendation.

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*Posted by John Quintanilla on October 8, 2016*

https://meangreenmath.com/2016/10/08/what-i-learned-from-reading-gamma-exploring-eulers-constant-by-julian-havil-part-8/

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