login
A258751
Decimal expansion of Ls_5(Pi), the value of the 5th basic generalized log-sine integral at Pi (negated).
10
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
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
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved