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

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, 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, 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

Offset: 0

Author

R. J. Mathar, Nov 24 2008

Keywords

• cons
• easy
• nonn

Comments

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.

Examples

			Equals 0.7553956195317414693865200287560823535149635906747...
		

References

• L. B. W. Jolley, Summation of Series, Dover (1961)

Links

• Anatol N. Kirillov, Dilogarithm identities, arXiv:hep-th/9408113.
• J. H. Loxton, Special values of the dilogarithm function, Acta Arithm. 43 (2) (1984), 155-166.

Programs

Mathematica

RealDigits[ PolyLog[2, (Sqrt[5]-1)/2], 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)

PARI

phic=(sqrt(5)-1)/2 ; dilog(phic);

Formula

Equals sum_{n>=1} x^n/n^2 for x= 2*sin(Pi/10). [Jolley eq (360d)]

Extensions

More terms from Jean-François Alcover, Feb 12 2013