A152651 Decimal expansion of 3*Zeta(5) - Zeta(3)*Pi^2/6.

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

Offset: 1

Author

R. J. Mathar, Dec 10 2008

Keywords

• cons
• easy
• nonn

Comments

A division by 2 is missing in Mezo's penultimate formula on page 4.

Examples

			Equals 1.1334789151328136607970110178859769320890912918456042272...
		

Links

• David Borwein and J. M. Borwein, On an intriguing integral and some series related to zeta(4), Proc. Am. Math. Soc. 123 (1995) 1191-1198.
• Istvan Mezo, Summation of Hyperharmonic Numbers, arXiv:0811.0042 [math.CO], 2008.

Programs

Mathematica

RealDigits[3*Zeta[5]-Zeta[3]*Pi^2/6,10,120][[1]] (* Harvey P. Dale, Apr 29 2019 *)

PARI

3*zeta(5) - zeta(3)*Pi^2/6 \\ Michel Marcus, Jul 07 2015

Formula

Equals Sum_(j >= 1) H(j)/j^4 = where H(j) = A001008(j)/A002805(j).

Equals 3*A013663 - A002117*A013661.