Definition:Euler-Mascheroni Constant/Historical Note

From ProofWiki
Jump to navigation Jump to search

Historical Note on Euler-Mascheroni Constant

The Euler-Mascheroni Constant was presented by Leonhard Paul Euler to the St. Petersburg Academy on $11$ March $1734$.

It was published in $1738$, calculated to $6$ decimal places, as $0 \cdotp 577218$ (although only the first $5$ were correct, as Euler himself surmised).

He subsequently calculated it to $16$ places in $1781$, and published this in $1785$.

Mascheroni published a calculation to $32$ places of the value of this constant.

Only the first $19$ places were accurate. The remaining ones were corrected in $1809$ by Johann von Soldner.

In more modern times, Dura W. Sweeney published the results of the calculation of its value to $3566$ places in $1963$.


There exists disagreement over the question of who was first to name it $\gamma$ (gamma).

Some sources claim it was Euler who named it $\gamma$, in $1781$, while others suggest its first appearance of that symbol for it was in Lorenzo Mascheroni's $1790$ work Adnotationes ad calculum integrale Euleri.

However, a close study of those works indicates that Euler used $A$ and $C$, and in the work cited, Mascheroni used $A$ throughout.

An early appearance of the symbol $\gamma$ was by Carl Anton Bretschneider in his $1837$ paper Theoriae logarithmi integralis lineamenta nova (J. reine angew. Math. Vol. 17: pp. 257 – 285), and this may indeed be the first.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Euler-Mascheroni_Constant/Historical_Note&oldid=628317"