A258751 Decimal expansion of Ls_5(Pi), the value of the 5th basic generalized log-sine integral at Pi (negated).

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

Offset: 2

Author

Jean-François Alcover, Jun 09 2015

Keywords

• nonn
• cons
• easy

Examples

			-24.22655837883478171663368704510531884635713927472260341881815179...
		

Links

• Jonathan M. Borwein, Armin Straub, Special Values of Generalized Log-sine Integrals.
• Index entries for transcendental numbers.

Crossrefs

Cf. A258749 (Ls_3(Pi)), A258750 (Ls_4(Pi)), A258752 (Ls_6(Pi)), A258753 (Ls_7(Pi)), A258754 (Ls_8(Pi)).

Programs

Mathematica

RealDigits[-19*Pi^5/240, 10, 105] // First

PARI

-19*Pi^5/240 \\ Charles R Greathouse IV, Nov 26 2024

Formula

-Integral_{0..Pi} log(2*sin(t/2))^4 dx = -19*Pi^5/240.

Also equals 4th derivative of -Pi*binomial(x, x/2) at x=0.