A393257 Decimal expansion of Pi*G, where G is Catalan's constant (A006752).

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

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

James G. Wan, Moments of products of elliptic integrals, Advances in Applied Mathematics, Vol. 48, No. 1 (2012), pp. 121-141; arXiv preprint, arXiv:1101.1132 [math.CA], 2011.

Formula

From Amiram Eldar, Feb 10 2026: (Start)

Equals Integral_{x=0..1} (arctanh(x)/x) * K(sqrt(1-x^2)) dx, where K(x) = (Pi/2) * hypergeom([1/2,1/2],[1],x^2) is the complete elliptic integral of the first kind (Wan, 2012, p. 128, in which "arctan" is a typo).

Equals 2 * Integral_{x=0..1} x * K(sqrt(1-x^2)) * K(i*x) dx, where i = sqrt(-1) (Wan, 2012, p. 129). (End)

Example

2.87759078160816115177758016652154780011485440005...

Mathematica

First[RealDigits[Pi*Catalan, 10, 100]]

Prog

(PARI) Pi * Catalan \\ Amiram Eldar, Feb 10 2026

Crossrefs

Cf. A000796, A006752, A143233.

Sequence in context: A083679 A213930 A394908 * A319463 A379711 A079031

Adjacent sequences: A393254 A393255 A393256 * A393258 A393259 A393261

Keyword

nonn,cons,easy

Author

Paolo Xausa, Feb 07 2026

Status

approved