A276627 Decimal expansion of K(3-2*sqrt(2)), where K is the complete elliptic integral of the first kind.

1, 5, 8, 2, 5, 5, 1, 7, 2, 7, 2, 2, 3, 7, 1, 5, 9, 1, 1, 8, 3, 3, 1, 3, 5, 0, 7, 1, 0, 7, 0, 4, 0, 9, 8, 7, 6, 5, 2, 9, 4, 8, 8, 1, 4, 9, 6, 1, 8, 7, 8, 9, 2, 4, 3, 4, 9, 7, 1, 6, 9, 4, 4, 8, 4, 7, 8, 2, 0, 8, 5, 3, 5, 1, 8, 6, 6, 6, 3, 5, 5, 1, 7, 3, 6, 2, 0, 9, 8, 1, 4, 0, 6, 5, 5, 4, 3, 2, 2, 2, 0, 0, 0, 4, 1

Offset

1,2

Comments

The modulus k=3-2*sqrt(2).

K(k_4) in the Mathworld link.

Links

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

Eric Weisstein's World of Mathematics, Elliptic Integral Singular Values

I. J. Zucker and G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319. Table 1 N=4.

Formula

Equals 2*(2+sqrt(2))*Pi^(3/2)/Gamma(-1/4)^2.

Equals A174968 * A062539 /2. - R. J. Mathar, Aug 18 2023

Equals A093341 * A201488 [Zucker] - R. J. Mathar, Jun 24 2024

Example

1.58255172722371591183313507107040987652948814961878924349716944847...

Maple

evalf(2*(2+sqrt(2))*Pi^(3/2)/GAMMA(-1/4)^2, 120); # Muniru A Asiru, Oct 08 2018

Mathematica

RealDigits[N[EllipticK[(3 - 2 Sqrt[2])^2], 105]][[1]]
RealDigits[2*(2+Sqrt[2])*Pi^(3/2)/Gamma[-1/4]^2, 10, 100][[1]] (* G. C. Greubel, Oct 08 2018 *)

Prog

(PARI) default(realprecision, 100); 2*(2+sqrt(2))*Pi^(3/2)/gamma(-1/4)^2 \\ G. C. Greubel, Oct 08 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2*(2+Sqrt(2))*Pi(R)^(3/2)/Gamma(-1/4)^2; // G. C. Greubel, Oct 08 2018

Crossrefs

Cf. A157259 (for 3-2*sqrt(2)).

Sequence in context: A110989 A099736 A256453 * A119420 A134469 A238166

Adjacent sequences: A276624 A276625 A276626 * A276628 A276629 A276630

Keyword

nonn,cons

Author

Benedict W. J. Irwin, Sep 07 2016

Status

approved