

A258754


Decimal expansion of Ls_8(Pi), the value of the 8th basic generalized logsine integral at Pi.


10



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

4,1


LINKS

Table of n, a(n) for n=4..108.
Jonathan M. Borwein, Armin Straub, Special Values of Generalized Logsine Integrals


FORMULA

Integral_{t=0..Pi} log(2*sin(t/2))^7 = (2835/4)*Pi*zeta(7) + (315/8)*Pi^3*zeta(5) + (133/32)*Pi^5*zeta(3).
Also equals 7th derivative of Pi*binomial(x, x/2) at x=0.


EXAMPLE

5040.03987911504516434562143833539315930537596167748200200213853916...


MATHEMATICA

RealDigits[(2835/4)*Pi*Zeta[7] + (315/8)*Pi^3*Zeta[5] + (133/32)*Pi^5*Zeta[3], 10, 105] // First


PROG

(PARI) intnum(t=0, Pi, log(2*sin(t/2))^7) \\ Hugo Pfoertner, Jul 22 2020


CROSSREFS

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)).
Sequence in context: A225424 A202626 A011995 * A175296 A076266 A350281
Adjacent sequences: A258751 A258752 A258753 * A258755 A258756 A258757


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jun 09 2015


STATUS

approved



