|
|
A257435
|
|
Decimal expansion of G(1/6), a generalized Catalan constant.
|
|
4
|
|
|
9, 0, 0, 4, 2, 4, 6, 0, 0, 3, 8, 9, 7, 0, 7, 7, 5, 7, 8, 5, 8, 8, 2, 7, 5, 8, 9, 0, 2, 9, 0, 4, 9, 4, 8, 5, 8, 2, 9, 9, 4, 3, 9, 5, 7, 6, 6, 6, 6, 1, 8, 7, 6, 5, 5, 9, 5, 1, 5, 7, 3, 1, 8, 3, 9, 1, 0, 5, 4, 4, 2, 0, 3, 6, 7, 5, 6, 5, 4, 7, 4, 9, 9, 6, 2, 3, 2, 3, 1, 5, 3, 0, 2, 5, 7, 1, 2, 4, 8, 2, 2, 8, 7, 8, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
G(s) = (Pi/4) * 3F2(1/2, 1/2-s, s+1/2; 1, 3/2; 1), with 2F1 the hypergeometric function.
G(s) = (1/(8*s))*(Pi + cos(Pi*s)*(psi(1/4 + s/2) - psi(3/4 + s/2))), where psi is the digamma function (PolyGamma).
G(1/6) = (3/4)*sqrt(3)*log(2).
|
|
EXAMPLE
|
0.900424600389707757858827589029049485829943957666618765595157318391...
|
|
MATHEMATICA
|
RealDigits[(3/4)*Sqrt[3]*Log[2], 10, 105] // First
N[Pi*HypergeometricPFQ[{1/3, 1/2, 2/3}, {1, 3/2}, 1]/4, 105] (* Vaclav Kotesovec, Apr 24 2015 *)
|
|
PROG
|
(Magma) SetDefaultRealField(RealField(100)); (3/4)*Sqrt(3)*Log(2); // G. C. Greubel, Aug 24 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|