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A064533 Decimal expansion of Landau-Ramanujan constant. 27
7, 6, 4, 2, 2, 3, 6, 5, 3, 5, 8, 9, 2, 2, 0, 6, 6, 2, 9, 9, 0, 6, 9, 8, 7, 3, 1, 2, 5, 0, 0, 9, 2, 3, 2, 8, 1, 1, 6, 7, 9, 0, 5, 4, 1, 3, 9, 3, 4, 0, 9, 5, 1, 4, 7, 2, 1, 6, 8, 6, 6, 7, 3, 7, 4, 9, 6, 1, 4, 6, 4, 1, 6, 5, 8, 7, 3, 2, 8, 5, 8, 8, 3, 8, 4, 0, 1, 5, 0, 5, 0, 1, 3, 1, 3, 1, 2, 3, 3, 7, 2, 1, 9, 3, 7, 2, 6, 9, 1, 2, 0, 7, 9, 2, 5, 9, 2, 6, 3, 4, 1, 8, 7, 4, 2, 0, 6, 4, 6, 7, 8, 0, 8, 4, 3, 2, 3, 0, 6, 3, 3, 1, 5, 4, 3, 4, 6, 2, 9, 3, 8, 0, 5, 3, 1, 6, 0, 5, 1, 7, 1, 1, 6, 9, 6, 3, 6, 1, 7, 7, 5, 0, 8, 8, 1, 9, 9, 6, 1, 2, 4, 3, 8, 2, 4, 9, 9, 4, 2, 7, 7, 6, 8, 3, 4, 6, 9, 0, 5, 1, 6, 2, 3, 5, 1, 3, 9, 2, 1, 8, 7, 1, 9, 6, 2, 0, 5, 6, 9, 0, 5, 3, 2, 9, 5, 6, 4, 4, 6, 7, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, pp. 52,60-66; MR 95e : 11028

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.

G. H. Hardy, "Ramanujan, Twelve lectures on subjects suggested by his life and work", Chelsea, 1940, pp. 60-63; MR 21 # 4881

LINKS

David E. G. Hare, Table of n, a(n) for n = 0..125078

S. R. Finch, Landau-Ramanujan Constant

S. R. Finch, On a Generalized Fermat-Wiles Equation

Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants, Feb 18 1996

Xavier Gourdon and Pascal Sebah, Constants and records of computation

David E. G. Hare, 125,079 digits of the Landau-Ramanujan constant

David E. G. Hare, Landau-Ramanujan constant up to 10000 digits

Institute of Physics, Constants - Landau-Ramanujan Constant

Simon Plouffe, Landau Ramanujan constant

Eric Weisstein's World of Mathematics, Ramanujan constant

Robert G. Wilson v, The first 15584 digits of the Landau-Ramanujan constant

Wikipedia, Landau-Ramanujan.

FORMULA

Victor Adamchik calculated 5100 digits of the Landau-Ramanujan constant using Mathematica (from Mathematica 4 demos):

LandauRamanujan[n_] := With[{K = Ceiling[Log[2, n*Log[3, 10]]]}, N[Product[(((1 - 2^(-2^k))*4^2^k*Zeta[2^k])/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^2^(-k - 1), {k, 1, K}]/Sqrt[2], n]];

EXAMPLE

0.76422365358922066299069873125009232811679054139340951472168667374...

MATHEMATICA

First@ RealDigits@ N[1/Sqrt@2 Product[((1 - 2^(-2^k)) 4^(2^k) Zeta[2^k]/(Zeta[2^k, 1/4] - Zeta[2^k, 3/4]))^(2^(-k - 1)), {k, 8}], 2^8] (* Robert G. Wilson v, Jul 01 2007 *)

CROSSREFS

Cf. A125776 = Continued fraction. [From Harry J. Smith, May 13 2009]

Sequence in context: A105419 A175996 A134982 * A131184 A021933 A154730

Adjacent sequences:  A064530 A064531 A064532 * A064534 A064535 A064536

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Oct 08 2001

EXTENSIONS

More references needed! Hardy and Wright? Gruber and Lekkerkerker?

More terms from Vladeta Jovovic, Oct 08 2001

STATUS

approved

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Last modified September 18 03:49 EDT 2014. Contains 246887 sequences.