Euler's constant (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Euler's constant" in English language version.

refsWebsite

Global rank English rank

33doi.org

2^nd place

16worldcat.org

5^th place

15arxiv.org

69^th place

59^th place

11wolfram.com

513^th place

537^th place

10semanticscholar.org

11^th place

8^th place

10nist.gov

355^th place

454^th place

8jstor.org

26^th place

20^th place

6books.google.com

3^rd place

5oeis.org

742^nd place

538^th place

3harvard.edu

18^th place

17^th place

2web.archive.org

1^st place

2projecteuclid.org

3,707^th place

2,409^th place

2imj-prg.fr

low place

2sciencedirect.com

149^th place

178^th place

2numberworld.org

low place

2ams.org

451^st place

277^th place

1anu.edu.au

942^nd place

597^th place

1free.fr

321^st place

724^th place

1maa.org

3,479^th place

2,444^th place

1springer.com

274^th place

309^th place

1utsa.edu

low place

9,359^th place

1t5k.org

low place

1nih.gov

4^th place

1uni-goettingen.de

2,594^th place

2,546^th place

1tu-darmstadt.de

low place

1earthlink.net

7,693^rd place

5,406^th place

1researchgate.net

120^th place

125^th place

1eudml.org

low place

1dbraulibrary.org.in

low place

1utrgv.edu

low place

1colgate.edu

low place

9,382^nd place

1degruyter.com

1,425^th place

1,138^th place

1royalsocietypublishing.org

1,993^rd place

3,231^st place

1zbmath.org

1,923^rd place

1,068^th place

1ucsc.edu

3,619^th place

2,621^st place

1ehfd.github.io

low place

1lri.fr

low place

ams.org

mathscinet.ams.org

Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.

ams.org

Brent, Richard P.; McMillan, Edwin M. (1980). "Some new algorithms for high-precision computation of Euler's constant". Mathematics of Computation. 34 (149): 305–312. doi:10.1090/S0025-5718-1980-0551307-4. ISSN 0025-5718.

anu.edu.au

maths-people.anu.edu.au

Brent, Richard P. (1994). "Ramanujan and Euler's Constant" (PDF). Proc. Symp. Applied Math. 48: 541–545.

arxiv.org

Lagarias 2013. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Caves, Carlton M.; Fuchs, Christopher A. (1996). "Quantum information: How much information in a state vector?". The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later. Israel Physical Society. arXiv:quant-ph/9601025. Bibcode:1996quant.ph..1025C. ISBN 9780750303941. OCLC 36922834.
See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society. 131 (11): 3335–3344. arXiv:math.NT/0209070. doi:10.1090/S0002-9939-03-07081-3. S2CID 91176597.
Aptekarev, A. I. (28 February 2009). "On linear forms containing the Euler constant". arXiv:0902.1768 [math.NT].
Pilehrood, Khodabakhsh Hessami; Pilehrood, Tatiana Hessami (2013-12-29), On a continued fraction expansion for Euler's constant, arXiv:1010.1420
Wolf, Marek (2019). "6+infinity new expressions for the Euler-Mascheroni constant". arXiv:1904.09855 [math.NT]. The above sum is real and convergent when zeros $\rho$ and complex conjugate ${\bar {\rho }}$ are paired together and summed according to increasing absolute values of the imaginary parts of $\rho$ . See formula 11 on page 3. Note the typographical error in the numerator of Wolf's sum over zeros, which should be 2 rather than 1.
Villarino, Mark B. (2007). "Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number". arXiv:0707.3950 [math.CA]. It would also be interesting to develop an expansion for n! into powers of m, a new Stirling expansion, as it were. See formula 1.8 on page 3.
Lagarias 2013, p. 13. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, $q$ -logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal. 12 (2): 225–244. arXiv:math.NT/0304021. doi:10.1007/s11139-006-0075-1. S2CID 1368088.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
Sondow, Jonathan (1 August 2005a). New Vacca-type rational series for Euler's constant and its 'alternating' analog $\log {\frac {4}{\pi }}$ . arXiv:math.NT/0508042.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π -2$ and into the formal enveloping series with rational coefficients only". J. Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Pilehrood, Khodabakhsh Hessami; Pilehrood, Tatiana Hessami (2008-08-04), Vacca-type series for values of the generalized-Euler-constant function and its derivative, arXiv:0808.0410
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B.
Sondow, Jonathan (2003). "An infinite product for $e γ$ via hypergeometric formulas for Euler's constant, $γ$ ". arXiv:math.CA/0306008.

books.google.com

Bretschneider 1837, " $γ = c$ = 0,5772156649015328606181120900823..." on p. 260.
De Morgan, Augustus (1836–1842). The differential and integral calculus. London: Baldwin and Craddoc. " $γ$ " on p. 578.
Finch, Steven R. (2003-08-18). Mathematical Constants. Cambridge University Press. ISBN 978-0-521-81805-6.
Conway, John H.; Guy, Richard (1998-03-16). The Book of Numbers. Springer Science & Business Media. ISBN 978-0-387-97993-9.
Lodge, A. (1904). "An approximate expression for the value of 1 + 1/2 + 1/3 + ... + 1/r". Messenger of Mathematics. 30: 103–107.
Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.

colgate.edu

math.colgate.edu

Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B.

dbraulibrary.org.in

Bromwich, Thomas John I'Anson (2005) [1908]. An Introduction to the Theory of Infinite Series (PDF) (3rd ed.). United Kingdom: American Mathematical Society. p. 460. See exercise 18.

degruyter.com

Oettinger, Ludwig (1862-01-01). "Ueber die richtige Werthbestimmung der Constante des Integrallogarithmus". Journal für die reine und angewandte Mathematik (in German). 60: 375–376. doi:10.1515/crll.1862.60.375. ISSN 1435-5345.

doi.org

Lagarias 2013. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Blagouchine, Iaroslav V. (2014-10-01). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. ISSN 1572-9303.
Rosser, J. Barkley; Schoenfeld, Lowell (1962). "Approximate formulas for some functions of prime numbers". Illinois Journal of Mathematics. 6 (1): 64–94. doi:10.1215/ijm/1255631807. ISSN 0019-2082.
Pintz, János (1997-04-01). "Very Large Gaps between Consecutive Primes". Journal of Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081. ISSN 0022-314X.
Connallon, Tim; Hodgins, Kathryn A. (October 2021). "Allen Orr and the genetics of adaptation". Evolution. 75 (11): 2624–2640. doi:10.1111/evo.14372. PMID 34606622. S2CID 238357410.
See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society. 131 (11): 3335–3344. arXiv:math.NT/0209070. doi:10.1090/S0002-9939-03-07081-3. S2CID 91176597.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.
Mahler, Kurt; Mordell, Louis Joel (4 June 1968). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Ram Murty, M.; Saradha, N. (2010). "Euler–Lehmer constants and a conjecture of Erdos". Journal of Number Theory. 130 (12): 2671–2681. doi:10.1016/j.jnt.2010.07.004. ISSN 0022-314X.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Haible, Bruno; Papanikolaou, Thomas (1998). "Fast multiprecision evaluation of series of rational numbers". In Buhler, Joe P. (ed.). Algorithmic Number Theory. Lecture Notes in Computer Science. Vol. 1423. Springer. pp. 338–350. doi:10.1007/bfb0054873. ISBN 9783540691136.
Brent, Richard P. (1977). "Computation of the Regular Continued Fraction for Euler's Constant". Mathematics of Computation. 31 (139): 771–777. doi:10.2307/2006010. ISSN 0025-5718. JSTOR 2006010.
Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 2011-06-04. Retrieved 2006-05-29.
Boya, L.J. (2008). "Another relation between π, e, γ and ζ(n)". Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 102 (2): 199–202. doi:10.1007/BF03191819. γ/2 in (10) reflects the residual (finite part) of ζ(1)/2, of course. See formulas 1 and 10.
Sondow, Jonathan (2005). "Double Integrals for Euler's Constant and $\textstyle {\frac {4}{\pi }}$ and an Analog of Hadjicostas's Formula". The American Mathematical Monthly. 112 (1): 61–65. doi:10.2307/30037385. JSTOR 30037385. Retrieved 2024-04-27.
Chen, Chao-Ping (2018). "Ramanujan's formula for the harmonic number". Applied Mathematics and Computation. 317: 121–128. doi:10.1016/j.amc.2017.08.053. ISSN 0096-3003. Retrieved 2024-04-27.
Whittaker, E.; Watson, G. (2021) [1902]. A Course of Modern Analysis (5th ed.). p. 271, 275. doi:10.1017/9781009004091. ISBN 9781316518939. See Examples 12.21 and 12.50 for exercises on the derivation of the integral form $\textstyle \int _{-1}^{0}\ln \Gamma (z+1)\,dz$ of the series $\textstyle \sum _{k=1}^{n}{\frac {\zeta (k)}{110_{k}}}=\ln({\sqrt {2\pi }})$ .
Lagarias 2013, p. 13. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Nelsen, R. B. (1991). "Proof without Words: Sum of Reciprocals of Triangular Numbers". Mathematics Magazine. 64 (3): 167. doi:10.1080/0025570X.1991.11977600.
Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, $q$ -logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal. 12 (2): 225–244. arXiv:math.NT/0304021. doi:10.1007/s11139-006-0075-1. S2CID 1368088.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
DeTemple, Duane W. (May 1993). "A Quicker Convergence to Euler's Constant". The American Mathematical Monthly. 100 (5): 468–470. doi:10.2307/2324300. ISSN 0002-9890. JSTOR 2324300.
Vacca, G. (1910). "A new analytical expression for the number π and some historical considerations". Bulletin of the American Mathematical Society. 16: 368–369. doi:10.1090/S0002-9904-1910-01919-4.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π -2$ and into the formal enveloping series with rational coefficients only". J. Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.
Choi, Junesang; Srivastava, H.M. (1 September 2010). "Integral Representations for the Euler–Mascheroni Constant $γ$ ". Integral Transforms and Special Functions. 21 (9): 675–690. doi:10.1080/10652461003593294. ISSN 1065-2469. S2CID 123698377.
Oettinger, Ludwig (1862-01-01). "Ueber die richtige Werthbestimmung der Constante des Integrallogarithmus". Journal für die reine und angewandte Mathematik (in German). 60: 375–376. doi:10.1515/crll.1862.60.375. ISSN 1435-5345.
"I. On the calculation of the numerical value of Euler's constant, which Professor Price, of Oxford, calls E". Proceedings of the Royal Society of London. 15: 429–432. 1867-12-31. doi:10.1098/rspl.1866.0100. ISSN 0370-1662.
Knuth, Donald E. (July 1962). "Euler's Constant to 1271 Places". Mathematics of Computation. 16 (79). American Mathematical Society: 275–281. doi:10.2307/2004048. JSTOR 2004048.
Sweeney, Dura W. (1963). "On the computation of Euler's constant". Mathematics of Computation. 17 (82): 170–178. doi:10.1090/S0025-5718-1963-0160308-X. ISSN 0025-5718. S2CID 120162114.
Beyer, W. A.; Waterman, M. S. (1974). "Error Analysis of a Computation of Euler's Constant". Mathematics of Computation. 28 (126): 599–604. doi:10.2307/2005935. ISSN 0025-5718. JSTOR 2005935.
Brent, Richard P.; McMillan, Edwin M. (1980). "Some new algorithms for high-precision computation of Euler's constant". Mathematics of Computation. 34 (149): 305–312. doi:10.1090/S0025-5718-1980-0551307-4. ISSN 0025-5718.

earthlink.net

home.earthlink.net

Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 2011-06-04. Retrieved 2006-05-29.

ehfd.github.io

"Euler-Mascheroni Constant". Polymath Collector. 15 February 2020.

eudml.org

Cesàro, E. (1885). "Sur la série harmonique". Nouvelles annales de mathématiques: Journal des candidats aux écoles polytechnique et normale (in French). 4. Carilian-Goeury et Vor Dalmont: 295–296.

free.fr

numbers.computation.free.fr

Sondow, Jonathan (2004). "The Euler constant: γ". Retrieved 2024-11-01.

harvard.edu

ui.adsabs.harvard.edu

Caves, Carlton M.; Fuchs, Christopher A. (1996). "Quantum information: How much information in a state vector?". The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later. Israel Physical Society. arXiv:quant-ph/9601025. Bibcode:1996quant.ph..1025C. ISBN 9780750303941. OCLC 36922834.
Mahler, Kurt; Mordell, Louis Joel (4 June 1968). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Blagouchine, Iaroslav V. (2018). "Three notes on Ser's and Hasse's representations for the zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A (#A3): 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B.

imj-prg.fr

webusers.imj-prg.fr

Waldschmidt, Michel (2023). "On Euler's Constant" (PDF). Sorbonne Université, Institut de Mathématiques de Jussieu, Paris.
Waldschmidt, Michel (2023). "Some of the most famous open problems in number theory" (PDF).

jstor.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Brent, Richard P. (1977). "Computation of the Regular Continued Fraction for Euler's Constant". Mathematics of Computation. 31 (139): 771–777. doi:10.2307/2006010. ISSN 0025-5718. JSTOR 2006010.
Sondow, Jonathan (2005). "Double Integrals for Euler's Constant and $\textstyle {\frac {4}{\pi }}$ and an Analog of Hadjicostas's Formula". The American Mathematical Monthly. 112 (1): 61–65. doi:10.2307/30037385. JSTOR 30037385. Retrieved 2024-04-27.
Sondow, Jonathan (2005). "Double integrals for Euler's constant and $\log {\frac {4}{\pi }}$ and an analog of Hadjicostas's formula". American Mathematical Monthly. 112 (1): 61–65. arXiv:math.CA/0211148. doi:10.2307/30037385. JSTOR 30037385.
DeTemple, Duane W. (May 1993). "A Quicker Convergence to Euler's Constant". The American Mathematical Monthly. 100 (5): 468–470. doi:10.2307/2324300. ISSN 0002-9890. JSTOR 2324300.
Knuth, Donald E. (July 1962). "Euler's Constant to 1271 Places". Mathematics of Computation. 16 (79). American Mathematical Society: 275–281. doi:10.2307/2004048. JSTOR 2004048.
Beyer, W. A.; Waterman, M. S. (1974). "Error Analysis of a Computation of Euler's Constant". Mathematics of Computation. 28 (126): 599–604. doi:10.2307/2005935. ISSN 0025-5718. JSTOR 2005935.

lri.fr

Melquiond, Guillaume; Nowak, W. Georg; Zimmermann, Paul. "Numerical approximation of the Masser-Gramain constant to four decimal digits" (PDF). Retrieved 2024-10-03.

maa.org

mathdl.maa.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.

nih.gov

pubmed.ncbi.nlm.nih.gov

Connallon, Tim; Hodgins, Kathryn A. (October 2021). "Allen Orr and the genetics of adaptation". Evolution. 75 (11): 2624–2640. doi:10.1111/evo.14372. PMID 34606622. S2CID 238357410.

nist.gov

dlmf.nist.gov

"DLMF: §5.17 Barnes' 𝐺-Function (Double Gamma Function) ‣ Properties ‣ Chapter 5 Gamma Function". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §2.5 Mellin Transform Methods ‣ Areas ‣ Chapter 2 Asymptotic Approximations". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §6.6 Power Series ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.32 Integral Representations ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.22 Integrals ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.8 Power Series ‣ Bessel Functions and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §10.24 Functions of Imaginary Order ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §11.6 Asymptotic Expansions ‣ Struve and Modified Struve Functions ‣ Chapter 11 Struve and Related Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §13.2 Definitions and Basic Properties ‣ Kummer Functions ‣ Chapter 11 Confluent Hypergeometric Functions". dlmf.nist.gov. Retrieved 2024-11-01.
"DLMF: §9.12 Scorer Functions ‣ Related Functions ‣ Chapter 9 Airy and Related Functions". dlmf.nist.gov. Retrieved 2024-11-01.

numberworld.org

Yee, Alexander J. (7 March 2011). "Large Computations". www.numberworld.org.
Yee, Alexander J. "Records Set by y-cruncher". www.numberworld.org. Retrieved 30 April 2018.
Yee, Alexander J. "y-cruncher - A Multi-Threaded Pi-Program". www.numberworld.org.

oeis.org

Sloane, N. J. A. (ed.). "Sequence A001620 (Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A002852 (Continued fraction for Euler's constant)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A302120 (Absolute value of the numerators of a series converging to Euler's constant)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A302121 (Denominators of a series converging to Euler's constant)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A073004 (Decimal expansion of exp(gamma))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

projecteuclid.org

Rosser, J. Barkley; Schoenfeld, Lowell (1962). "Approximate formulas for some functions of prime numbers". Illinois Journal of Mathematics. 6 (1): 64–94. doi:10.1215/ijm/1255631807. ISSN 0019-2082.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.

researchgate.net

Mortici, Cristinel (2010). "On the Stirling expansion into negative powers of a triangular number". Math. Commun. 15: 359–364.

royalsocietypublishing.org

"I. On the calculation of the numerical value of Euler's constant, which Professor Price, of Oxford, calls E". Proceedings of the Royal Society of London. 15: 429–432. 1867-12-31. doi:10.1098/rspl.1866.0100. ISSN 0370-1662.

sciencedirect.com

Pintz, János (1997-04-01). "Very Large Gaps between Consecutive Primes". Journal of Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081. ISSN 0022-314X.
Chen, Chao-Ping (2018). "Ramanujan's formula for the harmonic number". Applied Mathematics and Computation. 317: 121–128. doi:10.1016/j.amc.2017.08.053. ISSN 0096-3003. Retrieved 2024-04-27.

semanticscholar.org

api.semanticscholar.org

Lagarias 2013. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Connallon, Tim; Hodgins, Kathryn A. (October 2021). "Allen Orr and the genetics of adaptation". Evolution. 75 (11): 2624–2640. doi:10.1111/evo.14372. PMID 34606622. S2CID 238357410.
See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society. 131 (11): 3335–3344. arXiv:math.NT/0209070. doi:10.1090/S0002-9939-03-07081-3. S2CID 91176597.
Mahler, Kurt; Mordell, Louis Joel (4 June 1968). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Lagarias 2013, p. 13. Lagarias, Jeffrey C. (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 556. arXiv:1303.1856. doi:10.1090/s0273-0979-2013-01423-x. S2CID 119612431.
Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, $q$ -logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal. 12 (2): 225–244. arXiv:math.NT/0304021. doi:10.1007/s11139-006-0075-1. S2CID 1368088.
Ramaré, Olivier (2022). Excursions in Multiplicative Number Theory. Birkhäuser Advanced Texts: Basel Textbooks. Basel: Birkhäuser/Springer. p. 131. doi:10.1007/978-3-030-73169-4. ISBN 978-3-030-73168-7. MR 4400952. S2CID 247271545.
Choi, Junesang; Srivastava, H.M. (1 September 2010). "Integral Representations for the Euler–Mascheroni Constant $γ$ ". Integral Transforms and Special Functions. 21 (9): 675–690. doi:10.1080/10652461003593294. ISSN 1065-2469. S2CID 123698377.
Sweeney, Dura W. (1963). "On the computation of Euler's constant". Mathematics of Computation. 17 (82): 170–178. doi:10.1090/S0025-5718-1963-0160308-X. ISSN 0025-5718. S2CID 120162114.

springer.com

link.springer.com

Blagouchine, Iaroslav V. (2014-10-01). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. ISSN 1572-9303.

t5k.org

"Heuristics: Deriving the Wagstaff Mersenne Conjecture". t5k.org. Retrieved 2024-11-01.

tu-darmstadt.de

www-old.cdc.informatik.tu-darmstadt.de

Papanikolaou, T. (1997). Entwurf und Entwicklung einer objektorientierten Bibliothek für algorithmische Zahlentheorie (Thesis) (in German). Universität des Saarlandes.

ucsc.edu

scipp.ucsc.edu

Gourdon, Xavier; Sebah, Pascal (2004). "The Euler constant: γ" (PDF). scipp.ucsc.edu. Retrieved 2024-10-27.

uni-goettingen.de

num.math.uni-goettingen.de

"Eulers Constant". num.math.uni-goettingen.de. Retrieved 2024-10-19.

utrgv.edu

scholarworks.utrgv.edu

Berndt, Bruce C. (January 2008). "A fragment on Euler's constant in Ramanujan's lost notebook". South East Asian J. Math. & Math. Sc. 6 (2): 17–22.

utsa.edu

zakuski.utsa.edu

Robin, Guy (1984). "Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann" (PDF). Journal de mathématiques pures et appliquées. 63: 187–213.

web.archive.org

Davis, P. J. (1959). "Leonhard Euler's Integral: A Historical Profile of the Gamma Function". American Mathematical Monthly. 66 (10): 849–869. doi:10.2307/2309786. JSTOR 2309786. Archived from the original on 7 November 2012. Retrieved 3 December 2016.
Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 2011-06-04. Retrieved 2006-05-29.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Euler-Mascheroni Constant". mathworld.wolfram.com. Retrieved 2024-10-19.
Weisstein, Eric W. "Digamma Function". mathworld.wolfram.com. Retrieved 2024-10-30.
Weisstein, Eric W. "Stieltjes Constants". mathworld.wolfram.com. Retrieved 2024-11-01.
Weisstein, Eric W. "Logarithmic Integral". mathworld.wolfram.com. Retrieved 2024-11-01.
Weisstein, Eric W. "Mertens Theorem". mathworld.wolfram.com. Retrieved 2024-10-08.
Weisstein, Eric W. "Mertens Constant". mathworld.wolfram.com. Retrieved 2024-11-01.
Weisstein, Eric W. "Porter's Constant". mathworld.wolfram.com. Retrieved 2024-11-01.
Weisstein, Eric W. "Euler-Mascheroni Constant Digits". mathworld.wolfram.com. Retrieved 2024-10-19.
Weisstein, Eric W. "Euler-Mascheroni Constant Continued Fraction". mathworld.wolfram.com. Retrieved 2024-09-23.
Weisstein, Eric W. "Euler-Mascheroni Constant Approximations". mathworld.wolfram.com. Retrieved 2024-10-19.
Weisstein, Eric W. "Masser-Gramain Constant". mathworld.wolfram.com. Retrieved 2024-10-19.

worldcat.org

search.worldcat.org

Blagouchine, Iaroslav V. (2014-10-01). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. ISSN 1572-9303.
Rosser, J. Barkley; Schoenfeld, Lowell (1962). "Approximate formulas for some functions of prime numbers". Illinois Journal of Mathematics. 6 (1): 64–94. doi:10.1215/ijm/1255631807. ISSN 0019-2082.
Pintz, János (1997-04-01). "Very Large Gaps between Consecutive Primes". Journal of Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081. ISSN 0022-314X.
Caves, Carlton M.; Fuchs, Christopher A. (1996). "Quantum information: How much information in a state vector?". The Dilemma of Einstein, Podolsky and Rosen – 60 Years Later. Israel Physical Society. arXiv:quant-ph/9601025. Bibcode:1996quant.ph..1025C. ISBN 9780750303941. OCLC 36922834.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.
Ram Murty, M.; Saradha, N. (2010). "Euler–Lehmer constants and a conjecture of Erdos". Journal of Number Theory. 130 (12): 2671–2681. doi:10.1016/j.jnt.2010.07.004. ISSN 0022-314X.
Murty, M. Ram; Zaytseva, Anastasia (2013). "Transcendence of Generalized Euler Constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. JSTOR 10.4169/amer.math.monthly.120.01.048. S2CID 20495981.
Brent, Richard P. (1977). "Computation of the Regular Continued Fraction for Euler's Constant". Mathematics of Computation. 31 (139): 771–777. doi:10.2307/2006010. ISSN 0025-5718. JSTOR 2006010.
Chen, Chao-Ping (2018). "Ramanujan's formula for the harmonic number". Applied Mathematics and Computation. 317: 121–128. doi:10.1016/j.amc.2017.08.053. ISSN 0096-3003. Retrieved 2024-04-27.
DeTemple, Duane W. (May 1993). "A Quicker Convergence to Euler's Constant". The American Mathematical Monthly. 100 (5): 468–470. doi:10.2307/2324300. ISSN 0002-9890. JSTOR 2324300.
Choi, Junesang; Srivastava, H.M. (1 September 2010). "Integral Representations for the Euler–Mascheroni Constant $γ$ ". Integral Transforms and Special Functions. 21 (9): 675–690. doi:10.1080/10652461003593294. ISSN 1065-2469. S2CID 123698377.
Oettinger, Ludwig (1862-01-01). "Ueber die richtige Werthbestimmung der Constante des Integrallogarithmus". Journal für die reine und angewandte Mathematik (in German). 60: 375–376. doi:10.1515/crll.1862.60.375. ISSN 1435-5345.
"I. On the calculation of the numerical value of Euler's constant, which Professor Price, of Oxford, calls E". Proceedings of the Royal Society of London. 15: 429–432. 1867-12-31. doi:10.1098/rspl.1866.0100. ISSN 0370-1662.
Sweeney, Dura W. (1963). "On the computation of Euler's constant". Mathematics of Computation. 17 (82): 170–178. doi:10.1090/S0025-5718-1963-0160308-X. ISSN 0025-5718. S2CID 120162114.
Beyer, W. A.; Waterman, M. S. (1974). "Error Analysis of a Computation of Euler's Constant". Mathematics of Computation. 28 (126): 599–604. doi:10.2307/2005935. ISSN 0025-5718. JSTOR 2005935.
Brent, Richard P.; McMillan, Edwin M. (1980). "Some new algorithms for high-precision computation of Euler's constant". Mathematics of Computation. 34 (149): 305–312. doi:10.1090/S0025-5718-1980-0551307-4. ISSN 0025-5718.

zbmath.org

Fischer, Helmut; Zeller, Karl (1961). "Bernoullische Zahlen und Eulersche Konstante". zbmath.org (in German). Retrieved 2024-10-27.