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Decimal expansion of Landau-Ramanujan constant.

+0
9

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; cons; graph; listen)

	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.` `Philippe Flajolet and Ilan Vardi, Zeta function Expansions of Classical constants, Feb. 18, 1996` `G. H. Hardy, "Ramanujan, Twelve lectures on subjects suggested by his life and work", Chelsea, 1940, pp. 60-63; MR 21 # 4881`
	LINKS	`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` `Xavier Gourdon and Pascal Sebah, Constants and records of computation` `Dave Hare, Landau-Ramanujan constant up to 10000 digits` `Institute of Physics, Constants - Landau-Ramanujan Constant` `S. Plouffe, Landau Ramanujan constant` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics` `Robert G. Wilson v, The first 15584 digits of the Landau-Ramanujan constant` `Wikipedia, the free encyclopedia, Landau-Ramanujan.`
	FORMULA	`Victor Adamchik calculated 5100 digits of the Landau-Ramanujan constant using Mathematica (from Mathematica 4 demos): ! (LandauRamanujan[n_] := With[{K = [LeftCeiling]Log[2, n Log[3, 10]] [RightCeiling]}, N[ (1 / (AT)2 ) ( [Product] + (k = 1 ) % K (( ( ((1 - 2^(-2^k)) ) 4^(2^k) Zeta[2^k] ) / (Zeta[2^k, 1/4] - Zeta[2^k, 3/4] )))^(2^((-k)-1))), 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 (rgwv@rgwv.com), Jul 01 2007 *)`
	CROSSREFS	`Adjacent sequences: A064530 A064531 A064532 this_sequence A064534 A064535 A064536` `Sequence in context: A132714 A105419 A134982 this_sequence A021933 A131266 A021089`
	KEYWORD	`cons,nonn`
	AUTHOR	`njas, Oct 08 2001`
	EXTENSIONS	`More references needed! Hardy and Wright? Gruber and Lekkerkerker?` `More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 08 2001`

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Last modified October 13 20:18 EDT 2008. Contains 145016 sequences.

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