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HandWiki. Euler–Mascheroni Constant. Encyclopedia. Available online: https://encyclopedia.pub/entry/37825 (accessed on 30 September 2026).
HandWiki. Euler–Mascheroni Constant. Encyclopedia. Available at: https://encyclopedia.pub/entry/37825. Accessed September 30, 2026.
HandWiki. "Euler–Mascheroni Constant" Encyclopedia, https://encyclopedia.pub/entry/37825 (accessed September 30, 2026).
HandWiki. (2022, December 02). Euler–Mascheroni Constant. In Encyclopedia. https://encyclopedia.pub/entry/37825
HandWiki. "Euler–Mascheroni Constant." Encyclopedia. Web. 02 December, 2022.
Euler–Mascheroni Constant
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The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by [math]\displaystyle{ \log: }[/math] Here, [math]\displaystyle{ \lfloor x\rfloor }[/math] represents the floor function. The numerical value of the Euler–Mascheroni constant, to 50 decimal places, is: 0.57721566490153286060651209008240243104215933593992... 

euler–mascheroni numerical value harmonic series

References

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  7. See also Sondow, Jonathan (2003). "Criteria for irrationality of Euler's constant". Proceedings of the American Mathematical Society 131 (11). doi:10.1090/S0002-9939-03-07081-3.  https://dx.doi.org/10.1090%2FS0002-9939-03-07081-3
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  13. Krämer, Stefan (2005) (in de). Die Eulersche Konstante γ und verwandte Zahlen. University of Göttingen. 
  14. Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine 71. http://home.earthlink.net/~jsondow/id8.html. Retrieved 2006-05-29. 
  15. Sondow, Jonathan (2005), "Double integrals for Euler's constant and [math]\displaystyle{ \log \frac{\pi} }[/math] and an analog of Hadjicostas's formula", American Mathematical Monthly 112 (1), doi:10.2307/30037385  https://dx.doi.org/10.2307%2F30037385
  16. Sondow, Jonathan (1 August 2005a). New Vacca-type rational series for Euler's constant and its 'alternating' analog [math]\displaystyle{ \log \frac{\pi} }[/math]. 
  17. Sondow, Jonathan; Zudilin, Wadim (2006). "Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper". The Ramanujan Journal 12 (2). doi:10.1007/s11139-006-0075-1.  https://dx.doi.org/10.1007%2Fs11139-006-0075-1
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  19. Havil 2003, pp. 75–8.
  20. Blagouchine 2016.
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  22. Glaisher, James Whitbread Lee (1910). "On Dr. Vacca's series for γ". Q. J. Pure Appl. Math. 41. 
  23. Hardy, G.H. (1912). "Note on Dr. Vacca's series for γ". Q. J. Pure Appl. Math. 43. 
  24. Vacca, G. (1926). "Nuova serie per la costante di Eulero, C=0,577...". Rendiconti, Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche" (in it). Matematiche e Naturali 6 (3). 
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  27. Blagouchine, Iaroslav V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal 35 (1). doi:10.1007/s11139-013-9528-5. https://www.researchgate.net/publication/257381156. 
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  31. Sloane, N. J. A., ed. "Sequence A302121 (Denominators of a series converging to Euler's constant)". OEIS Foundation. https://oeis.org/A302121. 
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  34. Sondow, Jonathan (2003). "An infinite product for eγ via hypergeometric formulas for Euler's constant, γ". arXiv:math.CA/0306008. //arxiv.org/abs/math.CA/0306008
  35. Choi, Junesang; Srivastava, H.M. (1 September 2010). "Integral Representations for the Euler–Mascheroni Constant γ". Integral Transforms and Special Functions 21 (9). doi:10.1080/10652461003593294. ISSN 1065-2469.  https://dx.doi.org/10.1080%2F10652461003593294
  36. Sloane, N. J. A., ed. "Sequence A002852 (Continued fraction for Euler's constant)". OEIS Foundation. https://oeis.org/A002852. 
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  38. Knuth, Donald E. (July 1962). "Euler's Constant to 1271 Places". Mathematics of Computation (American Mathematical Society) 16 (79). https://www.jstor.org/stable/2004048?seq=1. 
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  40. Yee, Alexander J.. "Records Set by y-cruncher". http://www.numberworld.org/y-cruncher/records.html.  Yee, Alexander J.. "y-cruncher - A Multi-Threaded Pi-Program". http://www.numberworld.org/y-cruncher/. 
  41. "Euler-Mascheroni Constant". https://ehfd.github.io/world-record/euler-mascheroni-constant/. 
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