A258762 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A258762

Decimal expansion of Ls_6(Pi/3), the value of the 6th basic generalized log-sine integral at Pi/3.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

3,2

LINKS

Table of n, a(n) for n=3..105.

Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.

FORMULA

-Integral_{0..Pi/3} log(2*sin(x/2))^5 dx = (15/2)*Pi*zeta(5) + (35/36)*Pi^3*zeta(3) - (135/4)*Im(-PolyLog(6, (-1)^(1/3)) + PolyLog(6, -(-1)^(2/3))).

Also equals 120 * 7F6(1/2,1/2,...; 3/2,3/2,...; 1/4) (with 7F6 the hypergeometric function).

EXAMPLE

120.0207613710553001755048886391927614834489250443014689821689519463 ...

MATHEMATICA

RealDigits[120* HypergeometricPFQ[Table[1/2, {7}], Table[3/2, {6}], 1/4], 10, 103] // First

CROSSREFS

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Cf. A143298 (Ls_2(Pi/3)), A258759 (Ls_3(Pi/3)), A258760 (Ls_4(Pi/3)), A258761 (Ls_5(Pi/3)), A258763 (Ls_7(Pi/3)).

Sequence in context: A361015 A028959 A317642 * A079181 A093693 A224447

Adjacent sequences: A258759 A258760 A258761 * A258763 A258764 A258765

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jun 09 2015

STATUS

approved