A266576 Decimal expansion of a constant related to the asymptotics of A032302.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Dilogarithm

Eric Weisstein's MathWorld, Polylogarithm

Wikipedia, Polylogarithm

Formula

Pi^2/12 + log(2)^2 + Sum_{j>=1} (1 / (j^2 * 2^(2*j+1)).

Equals Pi^2/6 + log(2)^2/2 + polylog(2, -1/2).

Equals Pi^2/12 + log(2)^2 + polylog(2, 1/4)/2.

Equals -polylog(2, -2). - Vaclav Kotesovec, Jul 29 2019

Example

1.436746366883680946362902023893583354249956435654872102667243924865...

Maple

evalf(Pi^2/6 + log(2)^2/2 + polylog(2, -1/2), 120);
Digits :=100 ; evalf(dilog(3)) ; # R. J. Mathar, Jan 07 2021

Mathematica

RealDigits[Pi^2/12 + Log[2]^2 + PolyLog[2, 1/4]/2, 10, 120][[1]]
RealDigits[-PolyLog[2, -2], 10, 120][[1]] (* Vaclav Kotesovec, Jul 29 2019 *)

Prog

(PARI) Pi^2/6 + log(2)^2/2 + polylog(2, -1/2) \\ Michel Marcus, Jan 04 2016

Crossrefs

Cf. A032302.

Sequence in context: A290612 A292616 A071901 * A103476 A021700 A309516

Adjacent sequences: A266573 A266574 A266575 * A266577 A266578 A266579

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jan 04 2016

Status

approved