A344688 Decimal expansion of 3236 * Pi^9 / (55801305 * sqrt(3)).

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

Offset: 0

Author

Sean A. Irvine, Aug 17 2021

Keywords

• nonn
• cons

Examples

			0.998050195657077237227863822730...
		

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (310).

Links

• Michael I. Shamos, Shamos's catalog of the real numbers (2011).
• Index entries for transcendental numbers.

Crossrefs

Cf. A129404, A344778, A344727.

Programs

Mathematica

RealDigits[3236 * Pi^9 / (55801305 * Sqrt[3]), 10, 120][[1]] (* Amiram Eldar, Jun 12 2023 *)

Formula

Equals 2^2 * 809 * Pi^9 / (3^13 * 5 * 7 * sqrt(3)).

Equals 1 + Sum_{k>=1} ( 1/(3*k+1)^9 - 1/(3*k-1)^9 ).

Equals Product_{p prime} (1 - Kronecker(-3, p)/p^9)^(-1) = Product_{p prime != 3} (1 + (-1)^(p mod 3)/p^9)^(-1). - Amiram Eldar, Nov 06 2023