A255685 Decimal expansion of the alternating double sum U(3,1) = Sum_{i>=2} (Sum_{j=1..i-1} (-1)^(i+j)/(i^3*j)) (negated).

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

Offset

0,3

Links

Table of n, a(n) for n=0..102.

David Broadhurst, Feynman’s sunshine numbers, arXiv:1004.4238 [physics.pop-ph], 2010, p. 16.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 6.

Formula

Pi^4/180 + (Pi^2/12)*log(2)^2 - (1/12)*log(2)^4 - 2*Li_4(1/2).

Example

-0.117875999650509326841013950834137618715217513175975...

Mathematica

U[3, 1] = Pi^4/180 + (Pi^2/12)*Log[2]^2  - (1/12)*Log[2]^4 - 2*PolyLog[4, 1/2]; RealDigits[U[3, 1], 10, 103] // First

Prog

(PARI)
Pi^4/180 + (Pi^2/12)*log(2)^2  - (1/12)*log(2)^4 - 2*polylog(4, 1/2) \\ Gheorghe Coserea, Sep 30 2018

Crossrefs

Cf. A099218.

Sequence in context: A100264 A373026 A272877 * A154192 A011283 A179659

Adjacent sequences: A255682 A255683 A255684 * A255686 A255687 A255688

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 02 2015

Status

approved