A258749 Decimal expansion of Ls_3(Pi), the value of the 3rd basic generalized log-sine integral at Pi (negated).

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

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.

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: A220398 A352633 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