Editing Euler's constant (section)

== References ==
* {{cite journal |last=Bretschneider |first=Carl Anton |date=1837 |orig-date=1835 |title=Theoriae logarithmi integralis lineamenta nova |journal=Crelle's Journal |volume=17 |pages=257–285 |language=la |url=https://zenodo.org/record/1448830
}}
* {{cite book |last=Havil |first=Julian |date=2003 |title=Gamma: Exploring Euler's Constant |publisher=Princeton University Press |isbn=978-0-691-09983-5
}}
* {{cite journal |last=Lagarias |first=Jeffrey C. |date=2013 |title=Euler's constant: Euler's work and modern developments |journal=[[Bulletin of the American Mathematical Society]] |volume=50 |issue=4 |page=556 |doi=10.1090/s0273-0979-2013-01423-x |arxiv=1303.1856 |s2cid=119612431
}}
===Footnotes===
{{Reflist|refs=
<ref name=OEIS_A002852>{{Cite OEIS |A002852 |Continued fraction for Euler's constant}}</ref>

<ref name=DeMorgan183642>{{cite book |last=De Morgan |first=Augustus |author-link=Augustus De Morgan |date=1836–1842 |title=The differential and integral calculus |location=London |publisher=Baldwin and Craddoc |at="{{math|''γ''}}" on [https://books.google.com/books?id=95x4IrIcHrgC&pg=PA578 p. 578] }}</ref>

<ref name=CavesFuchs1996>{{cite book |last1=Caves |first1=Carlton M. |author-link1=Carlton M. Caves |last2=Fuchs |first2=Christopher A. |date=1996 |chapter=Quantum information: How much information in a state vector? |title=The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later |publisher=Israel Physical Society |isbn=9780750303941 |oclc=36922834 |arxiv=quant-ph/9601025 |bibcode=1996quant.ph..1025C}}</ref>

<ref name=HaiblePapanikolaou1998>{{Cite book |last1=Haible |first1=Bruno |last2=Papanikolaou |first2=Thomas |title=Algorithmic Number Theory |chapter=Fast multiprecision evaluation of series of rational numbers |date=1998 |editor-last=Buhler |editor-first=Joe P. |series=Lecture Notes in Computer Science |volume=1423 |publisher=Springer |pages=338–350 |doi=10.1007/bfb0054873 |isbn=9783540691136}}</ref>

<ref name=Papanikolaou1997>{{cite thesis |last=Papanikolaou |first=T. |date=1997 |title=Entwurf und Entwicklung einer objektorientierten Bibliothek für algorithmische Zahlentheorie |publisher=Universität des Saarlandes |url=https://www-old.cdc.informatik.tu-darmstadt.de/reports/reports/papa.diss.ps.gz |language=de}}</ref>

<ref name=Sondow2003a>See also {{cite journal |last1=Sondow |first1=Jonathan |date=2003 |title=Criteria for irrationality of Euler's constant |journal=Proceedings of the American Mathematical Society |volume=131 |issue=11 |pages=3335–3344 |doi=10.1090/S0002-9939-03-07081-3 |s2cid=91176597 |arxiv=math.NT/0209070 }}</ref>

<ref name=Mahler1968>{{Cite journal |last1=Mahler |first1=Kurt |date=4 June 1968 |title=Applications of a theorem by A. B. Shidlovski |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |volume=305 |issue=1481 |pages=149–173 |doi=10.1098/rspa.1968.0111 |bibcode=1968RSPSA.305..149M |s2cid=123486171|url=https://carmamaths.org/resources/mahler/docs/169.pdf}}</ref>

<ref name=RamMurtySaradha2010>{{Cite journal |last1=Ram Murty |first1=M. |first2=N. |last2=Saradha |date=2010 |title=Euler–Lehmer constants and a conjecture of Erdos |journal=Journal of Number Theory |volume=130 |issue=12 |pages=2671–2681 |doi=10.1016/j.jnt.2010.07.004 |issn=0022-314X |doi-access=free }}</ref>

<ref name=Aptekarev2009>{{cite arXiv |last=Aptekarev |first=A. I. |date=28 February 2009 |title=On linear forms containing the Euler constant |class=math.NT |eprint=0902.1768}}</ref>

<ref name=Rivoal2012>{{Cite journal |last=Rivoal |first=Tanguy |date=2012 |title=On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant |journal=Michigan Mathematical Journal |volume=61 |issue=2 |pages=239–254 |doi=10.1307/mmj/1339011525 |issn=0026-2285 |doi-access=free |url=https://projecteuclid.org/euclid.mmj/1339011525}}</ref>

<ref name=MurtyZaytseva2013>{{Cite journal |last1=Murty |first1=M. Ram |last2=Zaytseva |first2=Anastasia |date=2013 |title=Transcendence of Generalized Euler Constants |journal=The American Mathematical Monthly |volume=120 |issue=1 |pages=48–54 |doi=10.4169/amer.math.monthly.120.01.048 |jstor=10.4169/amer.math.monthly.120.01.048 |s2cid=20495981 |issn=0002-9890 |url=https://www.jstor.org/stable/10.4169/amer.math.monthly.120.01.048 }}</ref>

<ref name="Krämer2005">{{cite book |last1=Krämer |first1= Stefan |date=2005 |title=Die Eulersche Konstante {{math|<i>γ</i>}} und verwandte Zahlen |publisher=University of Göttingen |language=de }}</ref>

<ref name=Sondow1998>{{cite journal |last1=Sondow |first1=Jonathan |date=1998  |title=An antisymmetric formula for Euler's constant |journal=Mathematics Magazine |volume=71 |issue=3 |pages=219–220 |doi=10.1080/0025570X.1998.11996638 |access-date=2006-05-29 |url=http://home.earthlink.net/~jsondow/id8.html |archive-date=2011-06-04 |archive-url=https://web.archive.org/web/20110604123534/http://home.earthlink.net/~jsondow/id8.html}}</ref>

<ref name=Sondow2005>{{cite journal |last=Sondow |first=Jonathan |date=2005 |title=Double integrals for Euler's constant and <math>\log \frac{4}{\pi}</math> and an analog of Hadjicostas's formula |journal=[[American Mathematical Monthly]] |volume=112 |issue=1 |pages=61–65 |doi=10.2307/30037385 |jstor=30037385 |arxiv=math.CA/0211148}}</ref>

<ref name=Sondow2005a>{{cite book |last1= Sondow |first1=Jonathan |date=1 August 2005a |title=New Vacca-type rational series for Euler's constant and its 'alternating' analog <math>\log \frac{4}{\pi}</math> |arxiv=math.NT/0508042}}</ref>

<ref name=SondowZudilin2006>{{cite journal |last1=Sondow |first1=Jonathan |first2=Wadim |last2=Zudilin |date=2006 |title=Euler's constant, {{math|''q''}}-logarithms, and formulas of Ramanujan and Gosper |journal=The Ramanujan Journal |volume=12 |issue=2 |pages=225–244 |doi=10.1007/s11139-006-0075-1 |s2cid=1368088 |arxiv=math.NT/0304021}}</ref>

<ref name=DeTemple1993>{{cite journal |last=DeTemple |first=Duane W. |date=May 1993 |title=A Quicker Convergence to Euler's Constant |journal=The American Mathematical Monthly |volume=100 |issue=5 |pages=468–470 |doi=10.2307/2324300 |issn=0002-9890 |jstor=2324300}}</ref>

<ref name=Blagouchine2016>{{cite journal |last=Blagouchine |first=Iaroslav V. |date=2016 |title=Expansions of generalized Euler's constants into the series of polynomials in {{math|π<sup>−2</sup>}} and into the formal enveloping series with rational coefficients only |journal=[[Journal of Number Theory|J. Number Theory]] |volume=158 |pages=365–396 |doi=10.1016/j.jnt.2015.06.012 |arxiv=1501.00740}}</ref>

<ref name=Vacca1910>{{cite journal |last1=Vacca |first1=G. |author-link=Giovanni Vacca (mathematician) |date=1910 |title=A new analytical expression for the number π and some historical considerations |journal=Bulletin of the American Mathematical Society |volume=16 |pages=368–369|doi=10.1090/S0002-9904-1910-01919-4 |doi-access=free }}</ref>

<ref name=Vacca1926>{{cite journal |last1=Vacca |first1=G. |author-link=Giovanni Vacca (mathematician) |date=1926 |title=Nuova serie per la costante di Eulero, {{math|''C''}} = 0,577...". Rendiconti, Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche |journal=Matematiche e Naturali |volume=6 |issue=3 |pages=19–20 |language=it}}</ref>

<ref name=Glaisher1910>{{cite journal |last=Glaisher |first=James Whitbread Lee |author-link=James Whitbread Lee Glaisher |date=1910 |title=On Dr. Vacca's series for {{math|''γ''}} |journal=Q. J. Pure Appl. Math. |volume=41 |pages=365–368}}</ref>

<ref name=Hardy1912>{{ cite journal |last1= Hardy |first1=G.H. |date=1912 |title=Note on Dr. Vacca's series for {{math|''γ''}} |journal=Q. J. Pure Appl. Math. |volume=43 |pages=215–216}}</ref>

<ref name=Kluyver1927>{{cite journal |last1=Kluyver |first1=J.C. |date=1927 |title=On certain series of Mr. Hardy |journal=Q. J. Pure Appl. Math. |volume=50 |pages=185–192}}</ref>

<ref name=Blagouchine2018>{{cite journal |last1=Blagouchine |first1=Iaroslav V. |date=2018 |title=Three notes on Ser's and Hasse's representations for the zeta-functions |journal=INTEGERS: The Electronic Journal of Combinatorial Number Theory |volume=18A |issue=#A3 |pages=1–45 |doi=10.5281/zenodo.10581385 |bibcode=2016arXiv160602044B |arxiv=1606.02044 |url=http://math.colgate.edu/~integers/vol18a.html}}</ref>

<ref name=Alabdulmohsin2018_1478>{{cite book |last=Alabdulmohsin |first=Ibrahim M. |date=2018 |title=Summability Calculus. A Comprehensive Theory of Fractional Finite Sums |publisher=[[Springer Science+Business Media|Springer]] |pages=147–8 |isbn=9783319746487}}</ref>

<ref name=OEIS_A302120>{{cite OEIS|A302120|Absolute value of the numerators of a series converging to Euler's constant}}</ref>

<ref name=OEISA302121>{{cite OEIS|A302121|Denominators of a series converging to Euler's constant}}</ref>

<ref name=excursions>{{cite book
 | last = Ramaré | first = Olivier
 | doi = 10.1007/978-3-030-73169-4
 | isbn = 978-3-030-73168-7
 | location = Basel
 | mr = 4400952
 | page = 131
 | publisher = Birkhäuser/Springer
 | series = Birkhäuser Advanced Texts: Basel Textbooks
 | title = Excursions in Multiplicative Number Theory
 | url = https://books.google.com/books?id=n1piEAAAQBAJ&pg=PA131
 | year = 2022| s2cid = 247271545
 }}</ref>

<ref name=OEIS_A073004>{{cite OEIS|A073004|Decimal expansion of exp(gamma)}}</ref>

<ref name=ChoiSrivastava2010>{{Cite journal |last1=Choi |first1=Junesang |last2=Srivastava |first2=H.M. |date=1 September 2010 |title=Integral Representations for the Euler–Mascheroni Constant {{math|''γ''}} |journal=Integral Transforms and Special Functions |volume=21 |issue=9 |pages=675–690 |doi=10.1080/10652461003593294 |s2cid=123698377 |issn=1065-2469}}</ref>

<ref name=Sondow2003>{{cite arXiv |last1=Sondow |first1=Jonathan |date=2003 |eprint=math.CA/0306008 |title= An infinite product for {{math|''e{{sup|γ}}''}} via hypergeometric formulas for Euler's constant, {{math|''γ''}}}}</ref>

<ref name=Knuth1962>{{cite journal |last1=Knuth |first1=Donald E. |author-link=Donald Knuth |date=July 1962 |title=Euler's Constant to 1271 Places |journal=Mathematics of Computation |volume=16 |issue=79 |pages=275–281 |publisher=[[American Mathematical Society]] |doi=10.2307/2004048 |jstor=2004048 |url=https://www.jstor.org/stable/2004048}}</ref>

<ref name=Yee2011>{{cite web |last=Yee |first=Alexander J. |date=7 March 2011 |title=Large Computations |website=www.numberworld.org |url=http://www.numberworld.org/nagisa_runs/computations.html}}</ref>

<ref name=Y_cruncher>{{cite web |last=Yee |first=Alexander J. |title=Records Set by y-cruncher |website=www.numberworld.org |access-date=30 April 2018 |url=http://www.numberworld.org/y-cruncher/records.html }}<br/>
{{cite web |last=Yee |first=Alexander J. |title=y-cruncher - A Multi-Threaded Pi-Program |website=www.numberworld.org |url=http://www.numberworld.org/y-cruncher/}}</ref>

<ref name=MascheroniConst_PolCol>{{cite web |title=Euler-Mascheroni Constant |website=Polymath Collector |date=15 February 2020 |url=https://ehfd.github.io/world-record/euler-mascheroni-constant/}}</ref>

<ref name=ConnallonHodgins2021>{{cite journal
 | last1 = Connallon | first1 = Tim
 | last2 = Hodgins | first2 = Kathryn A.
 | date = October 2021
 | doi = 10.1111/evo.14372
 | issue = 11
 | journal = Evolution
 | pages = 2624–2640
 | title = Allen Orr and the genetics of adaptation
 | volume = 75| pmid = 34606622
 | s2cid = 238357410
 }}</ref>

<ref name=Berndt2008>{{cite journal |last1=Berndt |first1=Bruce C.|author-link=Bruce C. Berndt |date=January 2008 |title=A fragment on Euler's constant in Ramanujan's lost notebook |journal=South East Asian J. Math. & Math. Sc |volume=6 |issue=2 |pages=17–22 |doi= |jstor= |url=https://scholarworks.utrgv.edu/cgi/viewcontent.cgi?article=1130&context=mss_fac}}</ref>

<ref name=A001620>{{Cite OEIS|A001620|Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma}}</ref>

}}