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A262427 Decimal expansion of the complete elliptic integral of the first kind at sqrt(2 sqrt(2) - 2). 1
2, 3, 2, 7, 1, 8, 5, 1, 4, 2, 4, 3, 6, 5, 3, 8, 7, 5, 0, 6, 0, 5, 0, 3, 6, 2, 8, 5, 6, 1, 8, 3, 5, 7, 0, 7, 7, 5, 1, 5, 1, 8, 1, 7, 5, 8, 2, 3, 2, 5, 4, 1, 1, 7, 4, 7, 9, 3, 2, 0, 8, 1, 9, 9, 4, 4, 6, 1, 1, 8, 8, 2, 5, 7, 3, 1, 3, 6, 0, 4, 9, 5, 7, 8, 2, 2, 5, 9, 0, 0, 7, 0, 1, 1, 0, 6, 6, 1, 0, 5, 6, 2, 3, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

M. L. Glasser and V. E. Wood, A closed form evaluation of the elliptic integral, Math. Comp. 25 (1971), 535-536.

FORMULA

Equals Pi^(3/2)*sqrt(4 + 2*sqrt(2))/(4*Gamma(5/8)*Gamma(7/8)).

Also equals sqrt(2)*K(sqrt(2) - 1).

EXAMPLE

2.3271851424365387506050362856183570775151817582325411747932...

MAPLE

evalf(sqrt(2)*EllipticK(sqrt(2)-1), 120); # Vaclav Kotesovec, Sep 22 2015

MATHEMATICA

K[x_] := EllipticK[x^2/(x^2 - 1)]/Sqrt[1 - x^2]; RealDigits[ K[Sqrt[2 Sqrt[2] - 2]], 10, 105][[1]]

PROG

(PARI) ellk(k)=intnum(t=0, 1, 1/sqrt((1-t^2)*(1-(k*t)^2)))

sqrt(2)*ellk(sqrt(2)-1) \\ Charles R Greathouse IV, Apr 18 2016

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^(3/2)*Sqrt(4 + 2*Sqrt(2))/(4*Gamma(5/8)*Gamma(7/8)); // G. C. Greubel, Oct 07 2018

CROSSREFS

Cf. A130786.

Sequence in context: A109878 A104565 A144456 * A333986 A349664 A266258

Adjacent sequences:  A262424 A262425 A262426 * A262428 A262429 A262430

KEYWORD

cons,nonn

AUTHOR

Jean-François Alcover, Sep 22 2015

STATUS

approved

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)