A266576 Decimal expansion of Pi^2/12 + log(2)^2 + Sum_{j>=1} 1 / (j^2 * 2^(2*j+1)).

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

Comments

A constant related to the asymptotics of A032302.

Links

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

Eric Weisstein's World of Mathematics, Dilogarithm

Eric Weisstein's World of Mathematics, Polylogarithm

Wikipedia, Polylogarithm

Formula

Equals 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
(PARI) -dilog(-2) \\ Charles R Greathouse IV, Sep 08 2025

Crossrefs

Cf. A032302.

Sequence in context: A292616 A071901 A388197 * A103476 A021700 A309516

Adjacent sequences: A266573 A266574 A266575 * A266577 A266578 A266579

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jan 04 2016

Status

approved