# History Question re Euler's Constant $\gamma$

What used to be be called "Euler's Constant" (http://en.wikipedia.org/wiki/Eulers_constant) is now frequently called the "Euler-Mascheroni Constant".

I have tried to find out what contribution Mascheroni made that merited his name being added to Euler's. All I have been able to turn up is that Mascheroni calculated $\gamma$ to a few more decimal places than Euler but the calculation had errors.

I assume Mascheroni did more than this for many authors to use "Euler-Mascheroni" for the name of $\gamma$ ? Any information on what his contribution was would be appreciated.

• Does the third paragraph of www-history.mcs.st-andrews.ac.uk/Biographies/Mascheroni.html answer your question? – lhf Apr 25 '14 at 2:47
• I looked at that reference before posting my question. In my opinion it does not answer my question. – gjh Apr 25 '14 at 2:54
• I guess you'll have to read the source and make your mind about Mascheroni's contribution and the claim that "Mascheroni's work shows a deep understanding of Euler's calculus". See archive.org/details/adnotationesadc00mascgoog – lhf Apr 25 '14 at 3:00
• Lagarias says: At that time constants were often named after a person who had done the labor of computing them to the most digits.....In the current era, which credits the mathematical contributions, it seems most appropriate to name the constant after Euler alone. – Will Jagy Apr 25 '14 at 3:06
• I use "Euler-Mascheroni constant" because "Euler's constant" is slightly ambiguous to me - IIRC some people use this to mean $e$. – Qiaochu Yuan Apr 25 '14 at 15:57

Your investigation into Lorenzo Mascheroni’s role in the history of Euler’s constant $\gamma$ led to the correct conclusion. An authoritative historic and survey article on Euler’s constant is given in Jeffrey Lagarias’ paper “Euler’s Constant: Euler’s Work and Modern Developments” October 2013 Bulletin of the American Mathematical Society, 50(4), 527–628. If you haven’t already read Lagarias’ article, Mascheroni’s contribution is discussed in Section 2.6 on pages 555-556, and the article states that he merely contributed four more correct digits to Euler’s computed 15-digit approximation (but Mascheroni’s published expression contained 32 digits).
Lagarias mentions that at that point in history, it was not uncommon to name constants after the person who had gone through the “... labor of computing them to the most digits.” Lagarias’ historical exposition is quite detailed, and it seems unlikely that he would have omitted any more significant contribution that Mascheroni might have made regarding $\gamma.$ Given this, he says that it's probably most appropriate that $\gamma$ be named for Euler alone.
But if it turns out that the Grothendieck constant $k_R$ is the reciprocal of $\gamma$, I think that might warrant a hyphenated appellation. :)