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Search: id:A002852
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| A002852 |
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Continued fraction for Euler's constant (or Euler-Mascheroni constant) gamma.
(Formerly M0097 N0034)
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+0
13
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| 0, 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49, 4, 1, 65, 1, 4, 7, 11, 1, 399, 2, 1, 3, 2, 1, 2, 1, 5, 3, 2, 1, 10, 1, 1, 1, 1, 2, 1, 1, 3, 1, 4, 1, 1, 2, 5, 1, 3, 6, 2, 1, 2, 1, 1, 1, 2, 1, 3, 16, 8, 1, 1, 2, 16, 6, 1, 2, 2, 1, 7, 2, 1, 1, 1, 3, 1, 2, 1, 2
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
K. Y. Choong, D. E. Daykin and C. R. Rathbone, Rational approximations to pi, Math. Comp., 25 (1971), 387-392.
K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403.
D. E. Knuth, Euler's constant to 1271 places. Math. Comp. 16 1962 275-281.
R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959.
J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analogue 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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T. D. Noe, Table of n, a(n) for n=0..10000
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].
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
G. Xiao, Contfrac
Index entries for continued fractions for constants
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
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EXAMPLE
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0.577215664901532860606512090082402431042...
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MATHEMATICA
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ContinuedFraction[ EulerGamma, 100 ]
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PROGRAM
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(PARI) { default(realprecision, 11000); x=contfrac(Euler); for (n=0, 10000, write("b002852.txt", n, " ", x[n+1])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 14 2009]
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CROSSREFS
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Cf. A001620, the decimal expansion, which has many more references.
See also A073004 (exp(gamma)).
Adjacent sequences: A002849 A002850 A002851 this_sequence A002853 A002854 A002855
Sequence in context: A088931 A088980 A157333 this_sequence A099875 A079499 A166235
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KEYWORD
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nonn,cofr,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 08 2000
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