Search: id:A001620
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%I A001620 M3755 N1532
%S A001620 5,7,7,2,1,5,6,6,4,9,0,1,5,3,2,8,6,0,6,0,6,5,1,2,0,9,0,0,8,2,4,0,2,
%T A001620 4,3,1,0,4,2,1,5,9,3,3,5,9,3,9,9,2,3,5,9,8,8,0,5,7,6,7,2,3,4,8,8,4,
%U A001620 8,6,7,7,2,6,7,7,7,6,6,4,6,7,0,9,3,6,9,4,7,0,6,3,2,9,1,7,4,6,7,4,9
%N A001620 Decimal expansion of Euler's constant (or Euler-Mascheroni constant) 
               gamma.
%D A001620 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 3.
%D A001620 S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and 
               its Applications, vol. 94, Cambridge University Press, pp. 28-40
%D A001620 J. Havil, Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003.
%D A001620 D. E. Knuth, Euler's constant to 1271 places. Math. Comp. 16 1962 275-281.
%D A001620 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001620 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001620 D. W. Sweeney, On the computation of Euler's constant, Math. Comp., 17 
               (1963), 170-178.
%D A001620 J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an 
               analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
%D A001620 J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. 
               Math. Soc. 131 (2003) 3335-3344.
%D A001620 J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 
               71 (1998) 219-220.
%H A001620 Harry J. Smith, <a href="b001620.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A001620 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001620 J. Borwein, <a href="http://www.worldwideschool.org/library/books/sci/
               math/MiscellaneousMathematicalConstants/chap35.html">170000 digits 
               of Euler or gamma constant</a>
%H A001620 D. Bradley, <a href="http://arXiv.org/abs/math.CA/0505125">Ramanujan's 
               formula for the logarithmic derivative of the Gamma function</a>
%H A001620 R. P. Brent, <a href="http://wwwmaths.anu.edu.au/~brent/pub/pub139.html">
               Ramanujan and Euler's constant</a>
%H A001620 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=Gamma">Euler's constant</a>
%H A001620 Dave's Math Tables, <a href="http://math2.org/math/constants/gamma.htm">
               Gamma Constant</a>
%H A001620 Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/
               publist.html">Zeta function expansions of some classical constants</
               a>
%H A001620 X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/
               Constants/Gamma/gamma.html">The Euler's constant gamma</a>
%H A001620 Richard Kreckel, <a href="http://www.ginac.de/~kreckel/news.html">116 
               million digits of Euler's constant</a> (bzipped)
%H A001620 A. Krowne, PlanetMath.org, <a href="http://planetmath.org/encyclopedia/
               EulerMascheroniConstant.html">Euler's constant</a>
%H A001620 T. Papanikolaou, Plouffe's Inverter, <a href="http://pi.lacim.uqam.ca/
               piDATA/gamma.txt">Euler's constant to 1000000 decimals</a>
%H A001620 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/
               Cpaper19/page1.htm">A series for Euler's constant</a>, Messenger 
               of Math., 46 (1917), 73-80.
%H A001620 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/
               question/q327.htm">Question 327</a>, J. Ind. Math. Soc.
%H A001620 J. Sondow, <a href="http://arXiv.org/abs/math.CA/0306008">An infinite 
               product for e^gamma via hypergeometric formulas for Euler's constant, 
               gamma</a>
%H A001620 J. Sondow, <a href="http://arXiv.org/abs/math.NT/0211075">A hypergeometric 
               approach, via linear forms involving logarithms, to irrationality 
               criteria for Euler's constant</a>
%H A001620 J. Sondow and W. Zudilin, <a href="http://arXiv.org/abs/math.NT/0304021">
               Euler's constant, q-logarithms and formulas of Ramanujan and Gosper</
               a>
%H A001620 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Euler-MascheroniConstant.html">Link to a section of The World of 
               Mathematics.</a>
%H A001620 <a href="Sindx_Be.html#Beatty">Index entries for sequences related to 
               Beatty sequences</a>
%F A001620 Integrate_{x=0..1} -Ln(Ln(1/x)) dx. - (from Robert G. Wilson v Jan 04 
               2006)
%e A001620 .577215664901532860606512090082402431042...
%p A001620 Digits := 100; evalf(gamma);
%t A001620 RealDigits[ EulerGamma, 10, 105][[1]] (from Robert G. Wilson v Nov 01 
               2004)
%o A001620 (PARI) { default(realprecision, 20080); x=Euler; d=0; for (n=0, 20000, 
               x=(x-d)*10; d=floor(x); write("b001620.txt", n, " ", d)); } [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 15 2009]
%Y A001620 Cf. A002852 (continued fraction).
%Y A001620 See also A073004 (exp(gamma)).
%Y A001620 Sequence in context: A100554 A138306 A154802 this_sequence A101456 A084823 
               A117034
%Y A001620 Adjacent sequences: A001617 A001618 A001619 this_sequence A001621 A001622 
               A001623
%K A001620 nonn,cons,nice
%O A001620 0,1
%A A001620 N. J. A. Sloane (njas(AT)research.att.com).

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