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 A076390 Decimal expansion of lemniscate constant B. 6
 5, 9, 9, 0, 7, 0, 1, 1, 7, 3, 6, 7, 7, 9, 6, 1, 0, 3, 7, 1, 9, 9, 6, 1, 2, 4, 6, 1, 4, 0, 1, 6, 1, 9, 3, 9, 1, 1, 3, 6, 0, 6, 3, 3, 1, 6, 0, 7, 8, 2, 5, 7, 7, 9, 1, 3, 1, 8, 3, 7, 4, 7, 6, 4, 7, 3, 2, 0, 2, 6, 0, 7, 0, 7, 1, 9, 5, 7, 8, 3, 5, 4, 1, 7, 9, 4, 2, 7, 7, 8, 2, 4, 4, 8, 9, 6, 6, 9, 4, 6, 8, 7, 9, 5, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also decimal expansion of AGM(1,i)/(1+i). REFERENCES J. M. Borwein and P. B. Borwein, Pi and the AGM. LINKS Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 53. J. Todd, The lemniscate constants, Comm. ACM, 18 (1975), 14-19; 18 (1975), 462. J. Todd, The lemniscate constants, in Pi: A Source Book, pp. 412-417. Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean Wolfram Research, Arithmetic-Geometric Mean FORMULA Equals (2*Pi)^(-1/2)*GAMMA(3/4)^2. Also equals ee/sqrt(2)-1/2*sqrt(2*ee^2-Pi) where ee = EllipticE(1/2), or also prod_{m>=1} ((2*m)/(2*m-1))^(-1)^m. - Jean-François Alcover, Sep 02 2014, after Steven Finch. EXAMPLE AGM(1,i) = 0.59907011736779610371... + 0.59907011736779610371...*i MATHEMATICA RealDigits[ Chop[ N[ ArithmeticGeometricMean[1, I]/(1 + I), 111]]] [[1]] PROG (PARI) real(agm(1, I)/(1+I)) \\ Charles R Greathouse IV, Mar 03 2016 (PARI) (2*Pi)^(-1/2)*gamma(3/4)^2 \\ Michel Marcus, Nov 10 2017 CROSSREFS Cf. A076391, A076392. Sequence in context: A123600 A063623 A085566 * A147818 A147777 A086731 Adjacent sequences:  A076387 A076388 A076389 * A076391 A076392 A076393 KEYWORD nonn,cons AUTHOR Robert G. Wilson v, Oct 09 2002 EXTENSIONS Edited by N. J. A. Sloane, Nov 01 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified July 23 00:51 EDT 2018. Contains 312919 sequences. (Running on oeis4.)