|
|
A076788
|
|
Decimal expansion of Sum_{m>=1} (1/(2^m*m^2)).
|
|
23
|
|
|
5, 8, 2, 2, 4, 0, 5, 2, 6, 4, 6, 5, 0, 1, 2, 5, 0, 5, 9, 0, 2, 6, 5, 6, 3, 2, 0, 1, 5, 9, 6, 8, 0, 1, 0, 8, 7, 4, 4, 1, 9, 8, 4, 7, 4, 8, 0, 6, 1, 2, 6, 4, 2, 5, 4, 3, 4, 3, 4, 7, 0, 4, 7, 8, 7, 3, 1, 7, 1, 0, 4, 4, 0, 7, 1, 6, 8, 3, 2, 0, 0, 8, 1, 6, 8, 4, 0, 3, 1, 8, 5, 8, 7, 9, 1, 5, 8, 5, 7, 1, 8, 5, 6, 4, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Dilog function Li_2(1/2).
|
|
REFERENCES
|
L. B. W. Jolley, Summation of Series, Dover (1961), eq. (116) on page 22 and eq. (360c) on page 68.
L. Lewin, Polylogarithms and Associated Functions, North Holland (1981), A2.1(4).
|
|
LINKS
|
|
|
FORMULA
|
Equals 1 - (1+1/2)/2 + (1+1/2+1/3)/3 - ... [Jolley].
Equals Sum_{k>=1} (-1)^(k+1)*H(k)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
Equals Integral_{x=0..1} log(1+x)/(x*(1+x)) dx. (End)
|
|
EXAMPLE
|
0.5822405264650125059026563201596801087441984748...
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) \p 200 dilog(1/2) Pi^2/12-1/2*(log(2))^2
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|