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important results in the domain of factorial series. His representation of Euler's constant as a series of rational terms is well known. It was used in 1926 byFloor and ceiling functions (5,879 words) [view diff] exact match in snippet view article find links to article
into two sequences via the floor function. There are formulas for Euler's constant γ = 0.57721 56649 ... that involve the floor and ceiling, e.g. γ =Erdős–Graham problem (530 words) [view diff] exact match in snippet view article find links to article
known that, for this to be true, b {\displaystyle b} must be at least Euler's constant e {\displaystyle e} . Ernie Croot proved the conjecture as part ofHadjicostas's formula (464 words) [view diff] exact match in snippet view article find links to article
arXiv:math/0405478. Sondow, J. (2003). "Criteria for irrationality of Euler's constant". Proc. Amer. Math. Soc. 131: 3335–3344. doi:10.1090/S0002-9939-03-07081-3Princeton Science Library (689 words) [view diff] case mismatch in snippet view article find links to article
Accelerating Cosmos by Robert P. Kirshner (2002) Gamma: Exploring Euler's Constant by Julian Havil [de] (2003) Journey from the Center of the Sun by JackComplete graph (1,244 words) [view diff] exact match in snippet view article find links to article
{\displaystyle w_{n+2}=n!e_{n}=\lfloor en!\rfloor ,} where e refers to Euler's constant, and e n = ∑ k = 0 n 1 k ! . {\displaystyle e_{n}=\sum _{k=0}^{n}{\fracGompertz constant (641 words) [view diff] exact match in snippet view article find links to article
(2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254Constant problem (364 words) [view diff] case mismatch in snippet view article find links to article
"Numerical Results on the Transcendence of Constants Involving π, e, and Euler's Constant" (PDF). Mathematics of Computation. 50 (20): 275–281. doi:10Transcendental number (6,761 words) [view diff] exact match in snippet view article find links to article
1098/rspa.1968.0111. S2CID 123486171. Lagarias, Jeffrey C. (2013-07-19). "Euler's constant: Euler's work and modern developments". Bulletin of the American MathematicalGolomb–Dickman constant (693 words) [view diff] exact match in snippet view article find links to article
Press. pp. 284–286. ISBN 0-521-81805-2. Lagarias, Jeffrey (2013). "Euler's constant: Euler's work and modern developments". Bull. Amer. Math. Soc. 50 (4):John Wrench (686 words) [view diff] exact match in snippet view article find links to article
25 invited guests. Wrench, Jr., J. W. (1952). "A new calculation of Euler's constant". Mathematical Tables and Other Aids to Computation. 6: 255. ShanksDarkside communication group (746 words) [view diff] exact match in snippet view article find links to article
}{\frac {1}{n^{n}}}} (ISBN 978-4-87310-173-6) One million digits of the Euler's constant (オイラー定数1000000桁表, ISBN 978-4-87310-053-1) One million digits of theList of numbers (3,929 words) [view diff] exact match in snippet view article find links to article
(2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254Helmut Maier (555 words) [view diff] exact match in snippet view article find links to article
Maier's matrix method Maier's theorem Lagarias, Jeffrey (2013). "Euler's constant: Euler's work and modern developments". Bulletin of the American MathematicalKempner series (1,213 words) [view diff] case mismatch in snippet view article find links to article
"Kempner series". MathWorld. Havil, Julian (2003). Gamma: Exploring Euler's Constant. Princeton: Princeton University Press. ISBN 978-0-691-09983-5. KempnerEuclid's theorem (3,508 words) [view diff] case mismatch in snippet view article find links to article
paper of his former proof. Havil, Julian (2003). Gamma: Exploring Euler's Constant. Princeton University Press. pp. 28–29. ISBN 0-691-09983-9. FurstenbergEdray Herber Goins (1,013 words) [view diff] exact match in snippet view article find links to article
Washington) Ars Combin. 117 (2014) 2016 Riordan matrix representations of Euler's constant γ and Euler's number e (with Asamoah Nkwanta) International JournalRiemann–Siegel theta function (1,522 words) [view diff] exact match in snippet view article find links to article
}\left({\frac {z}{n}}-\log \left(1+{\frac {z}{n}}\right)\right),} where γ is Euler's constant. Substituting ( 2 i t + 1 ) / 4 {\displaystyle (2it+1)/4} for z andRichard P. Brent (701 words) [view diff] case mismatch in snippet view article find links to article
M. (1980). "Some New Algorithms for High-Precision Computation of Euler's Constant". Mathematics of Computation 34 (149) 305-312. Brent, Richard Peirce;Capacitance (4,188 words) [view diff] exact match in snippet view article find links to article
= d / 2 a , D > 1 {\textstyle D=d/2a,D>1} γ {\textstyle \gamma } : Euler's constant q = D + D 2 − 1 {\displaystyle q=D+{\sqrt {D^{2}-1}}} ψ q ( z ) = ∂Wheel factorization (3,055 words) [view diff] exact match in snippet view article find links to article
{\varphi (n)}{n}}\log \log n=e^{-\gamma }\sim 0.56145948,} where γ is Euler's constant. Thus phi(n) / n goes to zero slowly as n increases to infinity andProof that 22/7 exceeds π (2,784 words) [view diff] case mismatch in snippet view article find links to article
MR 2176249, Zbl 1181.11077 Havil, Julian (2003), Gamma. Exploring Euler's Constant, Princeton, NJ: Princeton University Press, p. 96, ISBN 0-691-09983-9Genetic drift (6,353 words) [view diff] exact match in snippet view article find links to article
}{m}}{\text{ if }}mN_{e}\gg 1\end{cases}}} where γ {\displaystyle \gamma } is Euler's constant. The first approximation represents the waiting time until the firstDifferential entropy (2,728 words) [view diff] exact match in snippet view article find links to article
{\Gamma (p)\Gamma (q)}{\Gamma (p+q)}}} is the beta function, and γE is Euler's constant.: 219–230 Many of the differential entropies are from.: 120–122 AsHarmonic series (mathematics) (6,165 words) [view diff] case mismatch in snippet view article
Julian (2003). "Chapter 2: The harmonic series". Gamma: Exploring Euler's Constant. Princeton University Press. pp. 21–25. ISBN 978-0-691-14133-6. OslerComputational complexity of mathematical operations (1,488 words) [view diff] exact match in snippet view article find links to article
Gauss–Legendre algorithm O ( M ( n ) log n ) {\displaystyle O(M(n)\log n)} Euler's constant, γ {\displaystyle \gamma } Sweeney's method (approximation in termsNatural logarithm of 2 (3,129 words) [view diff] exact match in snippet view article find links to article
PMC 1078033. PMID 16588339. 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-XSrinivasa Ramanujan (11,693 words) [view diff] case mismatch in snippet view article find links to article
numbers". Messenger Math. 45: 81–84. Ramanujan, S. (1916). "A Series for Euler's Constant γ". Messenger Math. 46: 73–80. Ramanujan, S. (1917). "On the expressionParticle in a box (5,982 words) [view diff] exact match in snippet view article find links to article
\left({\frac {4\pi \hbar \,e^{2(1-\gamma )}}{L\,p_{0}}}\right)} where γ is Euler's constant. The quantum mechanical entropic uncertainty principle states thatDirichlet eta function (3,707 words) [view diff] exact match in snippet view article find links to article
27 (2000), 29–34. Sondow, Jonathan (2005). "Double integrals for Euler's constant and ln 4/π and an analog of Hadjicostas's formula". Amer. Math. MonthlyLogarithm (11,600 words) [view diff] case mismatch in snippet view article find links to article
MR 1009558, section III.6 Havil, Julian (2003), Gamma: Exploring Euler's Constant, Princeton University Press, ISBN 978-0-691-09983-5, sections 11.5FEE method (2,243 words) [view diff] exact match in snippet view article find links to article
M. McMillan, Some new algorithms for high-precision computation of Euler's constant. Math. Comp., Vol. 34 (1980). http://www.ccas.ru/personal/karatsuba/divcenBasel problem (7,368 words) [view diff] case mismatch in snippet view article find links to article
{\displaystyle n\rightarrow \infty } . Havil, J. (2003), Gamma: Exploring Euler's Constant, Princeton, New Jersey: Princeton University Press, pp. 37–42 (ChapterHistory of statistics (7,628 words) [view diff] case mismatch in snippet view article find links to article
Association, 18 (143), 841-851 JSTOR 2965467 Havil J (2003) Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 157 C. S. Peirce (1873)Secondary measure (3,522 words) [view diff] exact match in snippet view article find links to article
first form. In the formulas below G is Catalan's constant, γ is the Euler's constant, β2n is the Bernoulli number of order 2n, H2n+1 is the harmonic numberDipole antenna (12,392 words) [view diff] exact match in snippet view article find links to article
57721566 … {\displaystyle \ \gamma _{e}=0.57721566\ \ldots \ } is Euler's constant. There is an equivalent alternate form favored by some authors thatList of unsolved problems in mathematics (19,634 words) [view diff] case mismatch in snippet view article find links to article
Weisstein at Wolfram MathWorld (all articles accessed 22 August 2024): Euler's Constant Catalan's Constant Apéry's Constant irrational numbers (Archived 2015-03-27Kinetic imaging (2,064 words) [view diff] exact match in snippet view article find links to article
of interest, J is the intensity of the attenuated radiation, "e" is Euler's constant, and D is the attenuation. The linear attenuation coefficient alongList of important publications in mathematics (10,409 words) [view diff] exact match in snippet view article find links to article
Euler–Maclaurin formula and the values of ζ(2n), a further study of Euler's constant (including its connection to the gamma function), and an applicationIrrationality measure (4,484 words) [view diff] exact match in snippet view article find links to article
irrationality measure for Liouville numbers and conditional measures for Euler's constant". arXiv:math/0307308. Waldschmidt, Michel (2004-01-24). "Open Diophantine