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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.

J. Todd, The lemniscate constants, Comm. ACM, 18 (1975), 14-19; 18 (1975), 462.

LINKS

Table of n, a(n) for n=0..104.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 53.

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-Fran├žois 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

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 June 29 01:20 EDT 2017. Contains 288855 sequences.