Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A001620
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A001620 Decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.
(Formerly M3755 N1532)
+0
119
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)
OFFSET

0,1

REFERENCES

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.

LINKS

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

FORMULA

Integrate_{x=0..1} -Ln(Ln(1/x)) dx. - (from Robert G. Wilson v Jan 04 2006)

EXAMPLE

.577215664901532860606512090082402431042...

MAPLE

Digits := 100; evalf(gamma);

MATHEMATICA

RealDigits[ EulerGamma, 10, 105][[1]] (from Robert G. Wilson v Nov 01 2004)

PROGRAM

(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]

CROSSREFS

Cf. A002852 (continued fraction).

See also A073004 (exp(gamma)).

Sequence in context: A100554 A138306 A154802 this_sequence A101456 A084823 A117034

Adjacent sequences: A001617 A001618 A001619 this_sequence A001621 A001622 A001623

KEYWORD

nonn,cons,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

page 1

Search completed in 0.003 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified December 18 21:37 EST 2009. Contains 171024 sequences.


AT&T Labs Research