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 A258749 Decimal expansion of Ls_3(Pi), the value of the 3rd basic generalized log-sine integral at Pi (negated). 11
 2, 5, 8, 3, 8, 5, 6, 3, 9, 0, 0, 2, 4, 9, 8, 5, 0, 1, 4, 6, 2, 3, 0, 2, 6, 2, 5, 5, 5, 9, 1, 7, 8, 2, 9, 3, 3, 5, 1, 8, 7, 7, 4, 0, 4, 7, 1, 5, 7, 0, 9, 2, 3, 0, 7, 8, 4, 5, 3, 7, 8, 1, 7, 5, 3, 1, 7, 1, 9, 9, 5, 7, 6, 4, 5, 5, 4, 7, 5, 5, 0, 3, 1, 3, 0, 5, 5, 8, 4, 1, 9, 3, 8, 3, 5, 7, 3, 8, 4, 9, 4, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals FORMULA -Integral_{0..Pi} log(2*sin(t/2))^2 dx = -Pi^3/12. Also equals 2nd derivative of -Pi*binomial(x, x/2) at x=0. It can be noticed that Ls_2(Pi) is 0, and that Ls_2(Pi/2) is Catalan's constant 0.915966... (A006752). EXAMPLE -2.5838563900249850146230262555917829335187740471570923078453781753171... MATHEMATICA RealDigits[-Pi^3/12, 10, 103] // First PROG (PARI) -Pi^3/12 \\ G. C. Greubel, Aug 23 2018 (MAGMA) R:= RealField(100); -Pi(R)^3/12; // G. C. Greubel, Aug 23 2018 CROSSREFS Cf. A258750 (Ls_4(Pi)), A258751 (Ls_5(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)). Sequence in context: A296430 A220398 A200225 * A056886 A197839 A021391 Adjacent sequences:  A258746 A258747 A258748 * A258750 A258751 A258752 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jun 09 2015 STATUS approved

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Last modified December 10 12:30 EST 2019. Contains 329895 sequences. (Running on oeis4.)