Editing Euler's constant (section)

== History ==
The constant first appeared in a 1734 paper by the Swiss mathematician [[Leonhard Euler]], titled ''De Progressionibus harmonicis observationes'' (Eneström Index 43), where he described it as "worthy of serious consideration".<ref name=":3" />{{sfn|Lagarias|2013}} Euler initially calculated the constant's value to 6 decimal places. In 1781, he calculated it to 16 decimal places. Euler used the notations {{math|''C''}} and {{math|''O''}} for the constant. The Italian mathematician [[Lorenzo Mascheroni]] attempted to calculate the constant to 32 decimal places, but made errors in the 20th–22nd and 31st–32nd decimal places; starting from the 20th digit, he calculated ...'''181'''12090082'''39''' when the correct value is ...'''065'''12090082'''40'''. In 1790, he used the notations {{math|''A''}} and {{math|''a''}} for the constant. Other computations were done by [[Johann Georg von Soldner|Johann von Soldner]] in 1809, who used the notation {{math|''H''}}. The notation {{math|''γ''}} appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time, perhaps because of the constant's connection to the [[gamma function]].{{sfn|Lagarias|2013}} For example, the German mathematician [[Carl Anton Bretschneider]] used the notation {{math|''γ''}} in 1835,{{sfn|Bretschneider|1837|loc="{{math|1=''γ'' = ''c''}} = {{gaps|0,577215|664901|532860|618112|090082|3...}}" on [https://books.google.com/books?hl=fi&id=OAoPAAAAIAAJ&pg=PA260 p. 260]}} and [[Augustus De Morgan]] used it in a textbook published in parts from 1836 to 1842.{{r|DeMorgan183642}} Euler's constant was also studied by the Indian mathematician [[Srinivasa Ramanujan]] who published one paper on it in 1917.<ref>{{Cite book |last=Brent |first=Richard P. |date=1994 |chapter=Ramanujan and Euler's Constant |title=Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics |series=Proceedings of Symposia in Applied Mathematics |chapter-url=https://maths-people.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf  |volume=48 |pages=541–545|doi=10.1090/psapm/048/1314887 |isbn=978-0-8218-0291-5 }}</ref> [[David Hilbert]] mentioned the irrationality of {{math|''γ''}} as an unsolved problem that seems "unapproachable" and, allegedly, the English mathematician [[G. H. Hardy|Godfrey Hardy]] offered to give up his Savilian Chair at [[Oxford]] to anyone who could prove this.<ref name=":3" />