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A258761 Decimal expansion of Ls_5(Pi/3), the value of the 5th basic generalized log-sine integral at Pi/3 (negated). 4
2, 4, 0, 1, 2, 5, 3, 3, 1, 2, 5, 5, 1, 6, 9, 1, 4, 6, 1, 5, 0, 1, 5, 7, 1, 3, 9, 6, 3, 6, 3, 1, 6, 2, 6, 7, 9, 5, 0, 2, 8, 8, 4, 8, 4, 1, 0, 6, 4, 6, 3, 1, 5, 0, 2, 1, 9, 0, 1, 6, 2, 0, 7, 8, 2, 3, 3, 9, 2, 9, 9, 8, 2, 1, 7, 6, 3, 6, 8, 1, 4, 4, 4, 7, 2, 8, 9, 5, 8, 5, 8, 6, 4, 9, 1, 9, 0, 0, 1, 6, 3, 5, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..104.

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

FORMULA

-Integral_{0..Pi/3} log(2*sin(x/2))^4 dx = -1543*Pi^5/19440 + 6*Gl_{4, 1}(Pi/3), where Gl is the multiple Glaisher function.

Also equals -24 * 6F5(1/2,1/2,1/2,1/2,1/2,1/2; 3/2,3/2,3/2,3/2,3/2; 1/4) (with 6F5 the hypergeometric function).

EXAMPLE

-24.01253312551691461501571396363162679502884841064631502190162...

MATHEMATICA

RealDigits[-24*HypergeometricPFQ[Table[1/2, {6}], Table[3/2, {5}], 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)), A258762 (Ls_6(Pi/3)), A258763 (Ls_7(Pi/3)).

Sequence in context: A309635 A130659 A083741 * A256245 A173004 A118343

Adjacent sequences:  A258758 A258759 A258760 * A258762 A258763 A258764

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 09 2015

STATUS

approved

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Last modified January 21 03:00 EST 2021. Contains 340332 sequences. (Running on oeis4.)