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Search: id:A001620
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| A001620 |
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Decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.
(Formerly M3755 N1532)
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+0
119
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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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.
S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 28-40
J. Havil, Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003.
D. E. Knuth, Euler's constant to 1271 places. Math. Comp. 16 1962 275-281.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. W. Sweeney, On the computation of Euler's constant, Math. Comp., 17 (1963), 170-178.
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.
J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003) 3335-3344.
J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 71 (1998) 219-220.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
J. Borwein, 170000 digits of Euler or gamma constant
D. Bradley, Ramanujan's formula for the logarithmic derivative of the Gamma function
R. P. Brent, Ramanujan and Euler's constant
C. K. Caldwell, The Prime Glossary, Euler's constant
Dave's Math Tables, Gamma Constant
Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants
X. Gourdon and P. Sebah, The Euler's constant gamma
Richard Kreckel, 116 million digits of Euler's constant (bzipped)
A. Krowne, PlanetMath.org, Euler's constant
T. Papanikolaou, Plouffe's Inverter, Euler's constant to 1000000 decimals
S. Ramanujan, A series for Euler's constant, Messenger of Math., 46 (1917), 73-80.
S. Ramanujan, Question 327, J. Ind. Math. Soc.
J. Sondow, An infinite product for e^gamma via hypergeometric formulas for Euler's constant, gamma
J. Sondow, A hypergeometric approach, via linear forms involving logarithms, to irrationality criteria for Euler's constant
J. Sondow and W. Zudilin, Euler's constant, q-logarithms and formulas of Ramanujan and Gosper
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Beatty sequences
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FORMULA
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Integrate_{x=0..1} -Ln(Ln(1/x)) dx. - (from Robert G. Wilson v Jan 04 2006)
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EXAMPLE
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.577215664901532860606512090082402431042...
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MAPLE
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Digits := 100; evalf(gamma);
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MATHEMATICA
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RealDigits[ EulerGamma, 10, 105][[1]] (from Robert G. Wilson v Nov 01 2004)
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PROGRAM
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(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]
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CROSSREFS
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Cf. A002852 (continued fraction).
See also A073004 (exp(gamma)).
Adjacent sequences: A001617 A001618 A001619 this_sequence A001621 A001622 A001623
Sequence in context: A114603 A100554 A138306 this_sequence A101456 A084823 A117034
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KEYWORD
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nonn,cons,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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