

A258749


Decimal expansion of Ls_3(Pi), the value of the 3rd basic generalized logsine 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
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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 Logsine Integrals
Index entries for transcendental numbers


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

JeanFrançois Alcover, Jun 09 2015


STATUS

approved



