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

Author

Benedict W. J. Irwin, Sep 07 2016

Keywords

• nonn
• cons

Comments

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

K(k_4) in the MathWorld link.

Examples

			1.58255172722371591183313507107040987652948814961878924349716944847...
		

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.

Crossrefs

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

Programs

Magma

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

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 *)

PARI

default(realprecision, 100); 2*(2+sqrt(2))*Pi^(3/2)/gamma(-1/4)^2 \\ G. C. Greubel, Oct 08 2018

PARI

ellK(3-sqrt(8)) \\ Charles R Greathouse IV, Feb 05 2025

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