A346728 Decimal expansion of 11 * Pi^4 / (768 * sqrt(2)).

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

Offset: 0

Author

Sean A. Irvine, Jul 30 2021

Keywords

• nonn
• cons

Examples

			0.98654286069397050390153449061672691096683375790950...
		

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, Eqs. (327), (344).

Links

• R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, Section 2.2 at m=8, r=2, s=4.
• Michael I. Shamos, Shamos's catalog of the real numbers (2011).
• Index entries for transcendental numbers.

Crossrefs

Cf. A328895, A346727, A346260, A346451.

Programs

Mathematica

RealDigits[11*Pi^4/(768*Sqrt[2]), 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

Formula

Equals 11 * Pi^4 / (2^8 * 3 * sqrt(2)).

Equals 1 + Sum_{k>=1} ( (-1)^k/(4*k-1)^4 + (-1)^k/(4*k+1) ).

Equals Sum_{k>=0} (-1)^floor((k+1)/2) / (2*k+1)^4.