A247450 Decimal expansion of c(4), a constant appearing in certain Euler double sums not expressible in terms of well-known constants.

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

Offset: 1

Author

Jean-François Alcover, Sep 17 2014

Keywords

• nonn
• cons
• easy

Examples

			2.117141734777039411129100226012451751917680766916084...
		

Links

• J. M. Borwein, I.J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17 c(4).

Crossrefs

Cf. A002162 c(1), A072691 c(2), A233091 c(3).

Programs

Mathematica

c[4] = (1/12)*((-Pi^2)*Log[2]^2 + Log[2]^4 + 24*PolyLog[4, 1/2] + 21*Log[2]*Zeta[3]); RealDigits[c[4], 10, 104] // First

Formula

c(n) = sum_{k=0..n-2} (n-2)!/k!*log(2)^k*Li_(n-k)(1/2) + log(2)^n/n.

c(4) = (1/12)*((-Pi^2)*log(2)^2 + log(2)^4 + 24*Li_4(1/2) + 21*log(2)*zeta(3)).