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

2,1

Links

Table of n, a(n) for n=2..106.

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))^4 dx = -19*Pi^5/240.

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

Example

-24.22655837883478171663368704510531884635713927472260341881815179...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A255671 A330590 A055097 * A280233 A279902 A331004

Adjacent sequences: A258748 A258749 A258750 * A258752 A258753 A258754

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 09 2015

Status

approved