A345204 Decimal expansion of 5/4 + Pi^2/8 + zeta(3).

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

Offset: 1

Author

Amiram Eldar, Jun 10 2021

Keywords

• nonn
• cons

Examples

			3.68575745329576411275404953649596888267919871824559...
		

Links

• Ovidiu Furdui, Series Involving Products of Two Harmonic Numbers, Mathematics Magazine, Vol. 84, No. 5 (2011), pp. 371-377.

Crossrefs

Cf. A001008, A002117, A002805, A111003, A218505, A345203.

Programs

Mathematica

RealDigits[5/4 + Pi^2/8 + Zeta[3], 10, 100][[1]]

PARI

5/4 + Pi^2/8 + zeta(3) \\ Stefano Spezia, Jan 30 2025

Formula

Equals Sum_{k>=1} H(k)*H(k+2)/(k*(k+2)), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number (Furdui, 2011).

Equals 5/4 + A111003 + A002117.