cp's OEIS Frontend

A152115 Decimal expansion of the dilogarithm of (the golden mean minus 1), Li_2(phi-1).

%I A152115 #12 Jun 02 2013 04:22:31
%S A152115 7,5,5,3,9,5,6,1,9,5,3,1,7,4,1,4,6,9,3,8,6,5,2,0,0,2,8,7,5,6,0,8,2,3,
%T A152115 5,3,5,1,4,9,6,3,5,9,0,6,7,4,7,8,0,1,9,1,8,2,6,0,3,3,7,0,8,9,3,2,2,0,
%U A152115 9,1,3,6,6,7,4,9,5,8,7,1,1,3,1,5,1,2,2,7,9,3,2,8,5,4,6,6,8,2,8,1,2,6,6,5,9
%N A152115 Decimal expansion of the dilogarithm of (the golden mean minus 1), Li_2(phi-1).
%C A152115 Equals Li_2(phic) = L(phic)-log(phic)*log(1-phic)/2 = A002388/10 - A002390^2, where Li_2(.) is the dilogarithm, L(.) is Roger's dilogarithm, where phic = phi-1 = A094214, where -log(phic)= A002390 = log(1-phic)/2.
%D A152115 L. B. W. Jolley, Summation of Series, Dover (1961)
%H A152115 Anatol N. Kirillov, <a href="http://arxiv.org/abs/hep-th/9408113">Dilogarithm identities</a>, arXiv:hep-th/9408113.
%H A152115 J. H. Loxton, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa43/aa4326.pdf">Special values of the dilogarithm function</a>, Acta Arithm. 43 (2) (1984), 155-166.
%F A152115 Equals sum_{n>=1} x^n/n^2 for x= 2*sin(Pi/10). [Jolley eq (360d)]
%e A152115 Equals 0.7553956195317414693865200287560823535149635906747...
%t A152115 RealDigits[ PolyLog[2, (Sqrt[5]-1)/2], 10, 105] // First (* _Jean-François Alcover_, Feb 12 2013 *)
%o A152115 (PARI) phic=(sqrt(5)-1)/2 ; dilog(phic);
%K A152115 cons,easy,nonn
%O A152115 0,1
%A A152115 _R. J. Mathar_, Nov 24 2008
%E A152115 More terms from _Jean-François Alcover_, Feb 12 2013