A370374 Decimal expansion of 2*log(2) - 4*Catalan/Pi.

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

Offset: 0

Author

R. J. Mathar, Jun 07 2024

Keywords

• nonn
• cons

Examples

			0.22005074499...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.7.2, p. 55.

Links

• Sheldon Yang, Some properties of Catalan's constant G, Internat. J. Math. Ed. Sci. Tech. 23 (4) (1992) 549-556, L*(0).

Crossrefs

Cf. A016627, A218387.

Programs

Maple

2*log(2)-4*Catalan/Pi ; evalf(%) ;

Mathematica

RealDigits[2*Log[2] - 4*Catalan/Pi, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)

PARI

2*log(2) - 4*Catalan/Pi \\ Amiram Eldar, Jun 10 2024

Formula

Equals Sum_{n>=1} ((2n-1)!!/(2n)!!)^2 / (2*n).

Equals A016627 - A218387.

Equals Sum_{k>=1} binomial(2*k,k)^2/(k*2^(4*k+1)) (see Finch). - Stefano Spezia, Nov 13 2024