A383674 Decimal expansion of Integral_{0..1} 1 / ((1+x^4) * sqrt(1-x^4)) dx.

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products (6th ed.), 2000, (eq. 3.146.1).

Formula

Equals Pi/8 + (sqrt(2)/4) * EllipticK(sqrt(2)/2).

Equals A383676 + A003881. - Amiram Eldar, Apr 22 2026

Example

1.048213470271754107424040320...

Mathematica

RealDigits[Pi/8 + (Sqrt[2]/4) * EllipticK[1/2], 10, 120][[1]] (* Amiram Eldar, Apr 22 2026 *)

Prog

(PARI) intnum(x=0, 1, 1 / ((1+x^4) * sqrt(1-x^4))) \\ Michel Marcus, May 04 2025

Crossrefs

Cf. A003881, A019675, A383676.

Sequence in context: A134484 A244641 A396338 * A274192 A021958 A200412

Adjacent sequences: A383671 A383672 A383673 * A383675 A383676 A383677

Keyword

nonn,cons

Author

Sean A. Irvine, May 04 2025

Status

approved